def download_search(info):
dltype = info["Submit"]
delim = "bracket"
com = r"\\" # single line comment start
com1 = "" # multiline comment start
com2 = "" # multiline comment end
filename = "elliptic_curves.gp"
mydate = time.strftime("%d %B %Y")
if dltype == "sage":
com = "#"
filename = "elliptic_curves.sage"
if dltype == "magma":
com = ""
com1 = "/*"
com2 = "*/"
delim = "magma"
filename = "elliptic_curves.m"
s = com1 + "\n"
s += com + " Elliptic curves downloaded from the LMFDB downloaded on %s.\n" % (mydate)
s += com + " Below is a list called data. Each entry has the form:\n"
s += com + " [[field_poly],[Weierstrass Coefficients, constant first in increasing degree]]\n"
s += "\n" + com2
s += "\n"
if dltype == "magma":
s += "P<x> := PolynomialRing(Rationals()); \n"
s += "data := ["
elif dltype == "sage":
s += "x = polygen(QQ) \n"
s += "data = [ "
else:
s += "data = [ "
s += "\\\n"
nf_dict = {}
res = db_ecnf().find(ast.literal_eval(info["query"]))
for f in res:
nf = str(f["field_label"])
# look up number field and see if we already have the min poly
if nf in nf_dict:
poly = nf_dict[nf]
else:
poly = str(WebNumberField(f["field_label"]).poly())
nf_dict[nf] = poly
entry = str(f["ainvs"])
entry = entry.replace("u", "")
entry = entry.replace("'", "")
s += "[[" + poly + "], " + entry + "],\\\n"
s = s[:-3]
s += "]\n"
if delim == "brace":
s = s.replace("[", "{")
s = s.replace("]", "}")
if delim == "magma":
s = s.replace("[", "[*")
s = s.replace("]", "*]")
s += ";"
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO, attachment_filename=filename, as_attachment=True)
def __init__(self):
logger.debug("Constructing an instance of ECstats")
self.ecdb = db_ecnf()
self._counts = {}
self._stats = {}
self._dstats = {}
self._sigstats = {}
def make_torsion_growth(self):
try:
tor_gro = self.tor_gro
self.torsion_growth_data_exists = True
except AttributeError:
self.torsion_growth_data_exists = False
return
self.tg = tg = {}
tg['data'] = tgextra = []
# find all base-changes of this curve in the database, if any
from lmfdb.ecnf.WebEllipticCurve import db_ecnf
bcs = [
res['label']
for res in db_ecnf().find({'base_change': self.lmfdb_label},
projection={
'label': True,
'_id': False
})
]
bcfs = [lab.split("-")[0] for lab in bcs]
for F, T in tor_gro.items():
tg1 = {}
tg1['bc'] = "Not in database"
if ":" in F:
F = F.replace(":", ".")
field_data = nf_display_knowl(F, getDBConnection(),
field_pretty(F))
deg = int(F.split(".")[0])
bcc = [x for x, y in zip(bcs, bcfs) if y == F]
if bcc:
from lmfdb.ecnf.main import split_full_label
F, NN, I, C = split_full_label(bcc[0])
tg1['bc'] = bcc[0]
tg1['bc_url'] = url_for('ecnf.show_ecnf',
nf=F,
conductor_label=NN,
class_label=I,
number=C)
else:
field_data = web_latex_split_on_pm(
coeff_to_poly(string2list(F)))
deg = F.count(",")
tg1['d'] = deg
tg1['f'] = field_data
tg1['t'] = '\(' + ' \\times '.join(
['\Z/{}\Z'.format(n) for n in T.split(",")]) + '\)'
tg1['m'] = 0
tgextra.append(tg1)
tgextra.sort(key=lambda x: x['d'])
tg['n'] = len(tgextra)
lastd = 1
for tg1 in tgextra:
d = tg1['d']
if d != lastd:
tg1['m'] = len([x for x in tgextra if x['d'] == d])
lastd = d
tg['maxd'] = max(db_ecstats().find_one({'_id':
'torsion_growth'})['degrees'])
def __init__(self):
logger.debug("Constructing an instance of ECstats")
self.ecdb = db_ecnf()
self._counts = {}
self._stats = {}
self._dstats = {}
self._sigstats = {}
def show_ecnf1(nf):
if nf == "1.1.1.1":
return redirect(url_for("ec.rational_elliptic_curves", **request.args))
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 50
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
query = {'field_label': nf_label}
cursor = db_ecnf().find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC),
('conductor_label', ASC), ('iso_nlabel', ASC),
('number', ASC)]).skip(start).limit(count)
bread = [('Elliptic Curves', url_for(".index")),
(nf_label, url_for('.show_ecnf1', nf=nf_label))]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'],
getDBConnection(),
field_pretty(e['field_label']))
info = {}
info['field'] = nf_label
info['query'] = query
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
#don't risk recomputing all the ecnf stats just to show curves for a single number field
#if nf_label:
#info['stats'] = ecnf_field_summary(nf_label)
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curves over %s' % field_pretty(nf_label)
return render_template("ecnf-search-results.html",
info=info,
credit=ecnf_credit,
bread=bread,
title=t,
learnmore=learnmore_list())
def random_curve():
E = random_object_from_collection(db_ecnf())
return redirect(
url_for(".show_ecnf",
nf=E['field_label'],
conductor_label=E['conductor_label'],
class_label=E['iso_label'],
number=E['number']), 307)
def index():
# if 'jump' in request.args:
# return show_ecnf1(request.args['label'])
if len(request.args) > 0:
return elliptic_curve_search(data=request.args)
bread = get_bread()
data = {}
nfs = db_ecnf().distinct("field_label")
nfs = ["2.0.4.1", "2.2.5.1", "3.1.23.1"]
data["fields"] = [(nf, field_pretty(nf)) for nf in nfs if int(nf.split(".")[2]) < 200]
return render_template("ecnf-index.html", title="Elliptic Curves over Number Fields", data=data, bread=bread)
def by_label(label):
"""
Searches for a specific elliptic curve isogeny class in the
curves collection by its label, which can be either a full
curve label (including the field_label component) or a full
class label. In either case the data will be obtained from
the curve in the database with number 1 in the class.
"""
#print "label = %s" % label
try:
if label[-1].isdigit():
data = db_ecnf().find_one({"label": label})
else:
data = db_ecnf().find_one({"label": label + "1"})
except AttributeError:
return "Invalid label" # caller must catch this and raise an error
if data:
return ECNF_isoclass(data)
return "Class not found" # caller must catch this and raise an error
def by_label(label):
"""
Searches for a specific elliptic curve isogeny class in the
curves collection by its label, which can be either a full
curve label (including the field_label component) or a full
class label. In either case the data will be obtained from
the curve in the database with number 1 in the class.
"""
#print "label = %s" % label
try:
if label[-1].isdigit():
data = db_ecnf().find_one({"label": label})
else:
data = db_ecnf().find_one({"label": label + "1"})
except AttributeError:
return "Invalid label" # caller must catch this and raise an error
if data:
return ECNF_isoclass(data)
return "Class not found" # caller must catch this and raise an error
def show_ecnf1(nf):
if nf == "1.1.1.1":
return redirect(url_for("ec.rational_elliptic_curves", **request.args))
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 50
nf_label = parse_field_string(nf)
query = {"field_label": nf_label}
cursor = db_ecnf().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort(
[
("field_label", ASC),
("conductor_norm", ASC),
("conductor_label", ASC),
("iso_label", ASC),
("number", ASC),
]
)
.skip(start)
.limit(count)
)
bread = [("Elliptic Curves", url_for(".index")), (nf_label, url_for(".show_ecnf1", nf=nf_label))]
res = list(res)
for e in res:
e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), e["field_label"])
info = {}
info["field"] = nf_label
info["query"] = query
info["curves"] = res # [ECNF(e) for e in res]
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
info["field_pretty"] = field_pretty
info["web_ainvs"] = web_ainvs
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
t = "Elliptic Curves over %s" % field_pretty(nf_label)
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def random_curve():
E = random_object_from_collection(db_ecnf())
return redirect(
url_for(
".show_ecnf",
nf=E["field_label"],
conductor_label=E["conductor_label"],
class_label=E["iso_label"],
number=E["number"],
),
301,
)
def show_ecnf1(nf):
if nf == "1.1.1.1":
return redirect(url_for("ec.rational_elliptic_curves", **request.args))
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 50
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
query = {'field_label': nf_label}
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count)
bread = [('Elliptic Curves', url_for(".index")),
(nf_label, url_for('.show_ecnf1', nf=nf_label))]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), field_pretty(e['field_label']))
info = {}
info['field'] = nf_label
info['query'] = query
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
#don't risk recomputing all the ecnf stats just to show curves for a single number field
#if nf_label:
#info['stats'] = ecnf_field_summary(nf_label)
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curves over %s' % field_pretty(nf_label)
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t, learnmore=learnmore_list())
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db_ecnf().find_one({'label':label}, {'_id':False})
if data is None:
return search_input_error()
import json
response = make_response(json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def download_ECNF_all(nf,conductor_label,class_label,number):
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf,conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
data = db_ecnf().find_one({'label':label}, {'_id':False})
if data is None:
return search_input_error()
import json
response = make_response(json.dumps(data))
response.headers['Content-type'] = 'text/plain'
return response
def make_torsion_growth(self):
try:
tor_gro = self.tor_gro
self.torsion_growth_data_exists = True
except AttributeError:
self.torsion_growth_data_exists = False
return
self.tg = tg = {}
tg['data'] = tgextra = []
# find all base-changes of this curve in the database, if any
from lmfdb.ecnf.WebEllipticCurve import db_ecnf
bcs = [res['label'] for res in db_ecnf().find({'base_change': self.lmfdb_label}, projection={'label': True, '_id': False})]
bcfs = [lab.split("-")[0] for lab in bcs]
for F, T in tor_gro.items():
tg1 = {}
tg1['bc'] = "Not in database"
if ":" in F:
F = F.replace(":",".")
field_data = nf_display_knowl(F, getDBConnection(), field_pretty(F))
deg = int(F.split(".")[0])
bcc = [x for x,y in zip(bcs, bcfs) if y==F]
if bcc:
from lmfdb.ecnf.main import split_full_label
F, NN, I, C = split_full_label(bcc[0])
tg1['bc'] = bcc[0]
tg1['bc_url'] = url_for('ecnf.show_ecnf', nf=F, conductor_label=NN, class_label=I, number=C)
else:
field_data = web_latex_split_on_pm(coeff_to_poly(string2list(F)))
deg = F.count(",")
tg1['d'] = deg
tg1['f'] = field_data
tg1['t'] = '\(' + ' \\times '.join(['\Z/{}\Z'.format(n) for n in T.split(",")]) + '\)'
tg1['m'] = 0
tgextra.append(tg1)
tgextra.sort(key = lambda x: x['d'])
tg['n'] = len(tgextra)
lastd = 1
for tg1 in tgextra:
d = tg1['d']
if d!=lastd:
tg1['m'] = len([x for x in tgextra if x['d']==d])
lastd = d
tg['maxd'] = max(db_ecstats().find_one({'_id': 'torsion_growth'})['degrees'])
def show_ecnf1(nf):
if request.args:
return elliptic_curve_search(data=request.args)
start = 0
count = 20
query = {'field_label' : nf}
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_label', ASC), ('number', ASC)]).skip(start).limit(count)
bread = [('Elliptic Curves', url_for(".index")),
(nf, url_for('.show_ecnf1', nf=nf))]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label'])
info = {}
info['field'] = nf
info['query'] = query
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curves over %s' % field_pretty(nf)
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [
c for c in db_ecnf().find({
'field_label': self.field_label,
'conductor_norm': self.conductor_norm,
'conductor_label': self.conductor_label,
'iso_nlabel': self.iso_nlabel
}).sort('number')
]
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database
if not hasattr(self, 'isogeny_matrix'):
# this would happen if the class is initiated with a curve
# which is not #1 in its class:
self.isogeny_matrix = self.db_curves[0].isogeny_matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
self.one_deg = ZZ(self.class_deg).is_prime()
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(Matrix(self.isogeny_matrix))
self.field = FIELD(self.field_label)
self.field_name = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label,
lmfdb.base.getDBConnection(),
self.field_name)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[
c['short_label'],
curve_url(c),
web_ainvs(self.field_label, c['ainvs'])
] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass",
nf=self.field_label,
conductor_label=self.conductor_label,
class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor",
nf=self.field_label,
conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
totally_real = sig[1] == 0
imag_quadratic = sig == [0, 1]
if totally_real:
self.hmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage',
field_label=self.field_label,
label=self.hmf_label)
if sig[0] <= 2:
self.urls['Lfunction'] = url_for(
"l_functions.l_function_ecnf_page",
field_label=self.field_label,
conductor_label=self.conductor_label,
isogeny_class_label=self.iso_label)
elif self.abs_disc**2 * self.conductor_norm < 40000:
# we shouldn't trust the Lfun computed on the fly for large conductor
self.urls['Lfunction'] = url_for(
"l_functions.l_function_hmf_page",
field=self.field_label,
label=self.hmf_label,
character='0',
number='0')
if imag_quadratic:
self.bmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.bmf_url = url_for('bmf.render_bmf_webpage',
field_label=self.field_label,
level_label=self.conductor_label,
label_suffix=self.iso_label)
self.urls['Lfunction'] = url_for(
"l_functions.l_function_ecnf_page",
field_label=self.field_label,
conductor_label=self.conductor_label,
isogeny_class_label=self.iso_label)
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label,
self.urls['hmf'])]
if imag_quadratic:
#self.friends += [('Bianchi Modular Form %s not available' % self.bmf_label, '')]
self.friends += [('Bianchi Modular Form %s' % self.bmf_label,
self.bmf_url)]
if 'Lfunction' in self.urls:
self.friends += [('L-function', self.urls['Lfunction'])]
else:
self.friends += [('L-function not available', "")]
self.properties = [('Base field', self.field_name),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label,
self.urls['class'])]
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [c for c in db_ecnf().find(
{'field_label': self.field_label, 'conductor_norm':
self.conductor_norm, 'conductor_label':
self.conductor_label, 'iso_nlabel': self.iso_nlabel}).sort('number')]
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, sage.rings.infinity.Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database if possible, else create it
if hasattr(self, 'isogeny_matrix'):
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
else:
self.isogeny_matrix = make_iso_matrix(self.db_curves)
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
self.field = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label, lmfdb.base.getDBConnection(), self.field)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[c['short_label'], curve_url(c), web_ainvs(self.field_label,c['ainvs'])] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass", nf=self.field_label, conductor_label=self.conductor_label, class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor", nf=self.field_label, conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
totally_real = sig[1] == 0
imag_quadratic = sig == [0,1]
if totally_real:
self.hmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage', field_label=self.field_label, label=self.hmf_label)
self.urls['Lfunction'] = url_for("l_functions.l_function_hmf_page", field=self.field_label, label=self.hmf_label, character='0', number='0')
if imag_quadratic:
self.bmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label, self.urls['hmf'])]
self.friends += [('L-function', self.urls['Lfunction'])]
if imag_quadratic:
self.friends += [('Bianchi Modular Form %s not available' % self.bmf_label, '')]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)
]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label, self.urls['class'])]
def download_search(info):
dltype = info['Submit']
delim = 'bracket'
com = r'\\' # single line comment start
com1 = '' # multiline comment start
com2 = '' # multiline comment end
filename = 'elliptic_curves.gp'
mydate = time.strftime("%d %B %Y")
if dltype == 'sage':
com = '#'
filename = 'elliptic_curves.sage'
if dltype == 'magma':
com = ''
com1 = '/*'
com2 = '*/'
delim = 'magma'
filename = 'elliptic_curves.m'
s = com1 + "\n"
s += com + ' Elliptic curves downloaded from the LMFDB downloaded on %s.\n'%(mydate)
s += com + ' Below is a list called data. Each entry has the form:\n'
s += com + ' [[field_poly],[Weierstrass Coefficients, constant first in increasing degree]]\n'
s += '\n' + com2
s += '\n'
if dltype == 'magma':
s += 'P<x> := PolynomialRing(Rationals()); \n'
s += 'data := ['
elif dltype == 'sage':
s += 'x = polygen(QQ) \n'
s += 'data = [ '
else:
s += 'data = [ '
s += '\\\n'
nf_dict = {}
res = db_ecnf().find(ast.literal_eval(info["query"]))
for f in res:
nf = str(f['field_label'])
# look up number field and see if we already have the min poly
if nf in nf_dict:
poly = nf_dict[nf]
else:
poly = str(WebNumberField(f['field_label']).poly())
nf_dict[nf] = poly
entry = str(f['ainvs'])
entry = entry.replace('u','')
entry = entry.replace('\'','')
s += '[[' + poly + '], ' + entry + '],\\\n'
s = s[:-3]
s += ']\n'
if delim == 'brace':
s = s.replace('[', '{')
s = s.replace(']', '}')
if delim == 'magma':
s = s.replace('[', '[*')
s = s.replace(']', '*]')
s += ';'
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=filename,
as_attachment=True)
def download_search(info):
dltype = info['Submit']
delim = 'bracket'
com = r'\\' # single line comment start
com1 = '' # multiline comment start
com2 = '' # multiline comment end
filename = 'elliptic_curves.gp'
mydate = time.strftime("%d %B %Y")
if dltype == 'sage':
com = '#'
filename = 'elliptic_curves.sage'
if dltype == 'magma':
com = ''
com1 = '/*'
com2 = '*/'
delim = 'magma'
filename = 'elliptic_curves.m'
s = com1 + "\n"
s += com + ' Elliptic curves downloaded from the LMFDB downloaded on %s.\n' % (
mydate)
s += com + ' Below is a list called data. Each entry has the form:\n'
s += com + ' [[field_poly],[Weierstrass Coefficients, constant first in increasing degree]]\n'
s += '\n' + com2
s += '\n'
if dltype == 'magma':
s += 'P<x> := PolynomialRing(Rationals()); \n'
s += 'data := ['
elif dltype == 'sage':
s += 'x = polygen(QQ) \n'
s += 'data = [ '
else:
s += 'data = [ '
s += '\\\n'
nf_dict = {}
res = db_ecnf().find(ast.literal_eval(info["query"]))
for f in res:
nf = str(f['field_label'])
# look up number field and see if we already have the min poly
if nf in nf_dict:
poly = nf_dict[nf]
else:
poly = str(WebNumberField(f['field_label']).poly())
nf_dict[nf] = poly
entry = str(f['ainvs'])
entry = entry.replace('u', '')
entry = entry.replace('\'', '')
entry = entry.replace(';', '],[')
s += '[[' + poly + '], [[' + entry + ']]],\\\n'
s = s[:-3]
s += ']\n'
if delim == 'brace':
s = s.replace('[', '{')
s = s.replace(']', '}')
if delim == 'magma':
s = s.replace('[', '[*')
s = s.replace(']', '*]')
s += ';'
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=filename,
as_attachment=True,
add_etags=False)
def elliptic_curve_search(**args):
info = to_dict(args["data"])
if "download" in info and info["download"] != 0:
return download_search(info)
if not "query" in info:
info["query"] = {}
bread = [("Elliptic Curves", url_for(".index")), ("Search Results", ".")]
if "jump" in info:
label = info.get("label", "").replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except ValueError:
info["err"] = ""
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
try:
parse_ints(info, query, "conductor_norm")
parse_noop(info, query, "conductor_label")
parse_nf_string(info, query, "field", name="base number field", qfield="field_label")
parse_nf_elt(info, query, "jinv", name="j-invariant")
parse_ints(info, query, "torsion", name="Torsion order", qfield="torsion_order")
parse_bracketed_posints(info, query, "torsion_structure", maxlength=2)
if "torsion_structure" in query and not "torsion_order" in query:
query["torsion_order"] = reduce(mul, [int(n) for n in query["torsion_structure"]], 1)
except ValueError:
return search_input_error(info, bread)
if "include_isogenous" in info and info["include_isogenous"] == "off":
info["number"] = 1
query["number"] = 1
if "include_base_change" in info and info["include_base_change"] == "off":
query["base_change"] = []
else:
info["include_base_change"] = "on"
if "include_Q_curves" in info:
if info["include_Q_curves"] == "exclude":
query["q_curve"] = False
elif info["include_Q_curves"] == "only":
query["q_curve"] = True
if "include_cm" in info:
if info["include_cm"] == "exclude":
query["cm"] = 0
elif info["include_cm"] == "only":
query["cm"] = {"$ne": 0}
info["query"] = query
count = parse_count(info, 50)
start = parse_start(info)
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort(
[
("field_label", ASC),
("conductor_norm", ASC),
("conductor_label", ASC),
("iso_nlabel", ASC),
("number", ASC),
]
)
.skip(start)
.limit(count)
)
res = list(res)
for e in res:
e["numb"] = str(e["number"])
e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), field_pretty(e["field_label"]))
info["curves"] = res # [ECNF(e) for e in res]
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
info["field_pretty"] = field_pretty
info["web_ainvs"] = web_ainvs
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
t = "Elliptic Curve search results"
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label)
except IndexError:
if not 'query' in info:
info['query'] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [('Elliptic Curves', url_for(".index")),
('Search Results', '.')]
if 'conductor_norm' in info:
Nnorm = clean_input(info['conductor_norm'])
Nnorm = Nnorm.replace('..', '-').replace(' ', '')
tmp = parse_range2(Nnorm, 'conductor_norm')
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'conductor_label' in info:
query['conductor_label'] = info['conductor_label']
if 'jinv' in info:
query['jinv'] = info['jinv']
if info.get('torsion'):
ran = info['torsion'] = clean_input(info['torsion'])
ran = ran.replace('..', '-').replace(' ', '')
if not LIST_RE.match(ran):
info['err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).'
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, 'torsion_order')
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'torsion_structure' in info and info['torsion_structure']:
info['torsion_structure'] = clean_input(info['torsion_structure'])
if not TORS_RE.match(info['torsion_structure']):
info['err'] = 'Error parsing input for the torsion structure. It needs to be one or more integers in square brackets, such as [6], [2,2], or [2,4]. Moreover, each integer should be bigger than 1, and each divides the next.'
return search_input_error(info, bread)
query['torsion_structure'] = parse_list(info['torsion_structure'])
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
if 'field' in info:
query['field_label'] = parse_field_string(info['field'])
info['query'] = query
# process count and start if not default:
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_label', ASC), ('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label'])
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [c for c in db_ecnf().find(
{'field_label': self.field_label, 'conductor_norm':
self.conductor_norm, 'conductor_label':
self.conductor_label, 'iso_nlabel': self.iso_nlabel}).sort('number')]
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database
if not hasattr(self, 'isogeny_matrix'):
# this would happen if the class is initiated with a curve
# which is not #1 in its class:
self.isogeny_matrix = self.db_curves[0].isogeny_matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
self.one_deg = ZZ(self.class_deg).is_prime()
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(Matrix(self.isogeny_matrix))
self.field = FIELD(self.field_label)
self.field_name = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label, lmfdb.base.getDBConnection(), self.field_name)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[c['short_label'], curve_url(c), web_ainvs(self.field_label,c['ainvs'])] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass", nf=self.field_label, conductor_label=self.conductor_label, class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor", nf=self.field_label, conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
totally_real = sig[1] == 0
imag_quadratic = sig == [0,1]
if totally_real:
self.hmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage', field_label=self.field_label, label=self.hmf_label)
if sig[0] <= 2:
self.urls['Lfunction'] = url_for("l_functions.l_function_ecnf_page", field_label=self.field_label, conductor_label=self.conductor_label, isogeny_class_label=self.iso_label)
elif self.abs_disc ** 2 * self.conductor_norm < 40000:
# we shouldn't trust the Lfun computed on the fly for large conductor
self.urls['Lfunction'] = url_for("l_functions.l_function_hmf_page", field=self.field_label, label=self.hmf_label, character='0', number='0')
if imag_quadratic:
self.bmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.bmf_url = url_for('bmf.render_bmf_webpage', field_label=self.field_label, level_label=self.conductor_label, label_suffix=self.iso_label)
self.urls['Lfunction'] = url_for("l_functions.l_function_ecnf_page", field_label=self.field_label, conductor_label=self.conductor_label, isogeny_class_label=self.iso_label)
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label, self.urls['hmf'])]
if imag_quadratic:
#self.friends += [('Bianchi Modular Form %s not available' % self.bmf_label, '')]
self.friends += [('Bianchi Modular Form %s' % self.bmf_label, self.bmf_url)]
if 'Lfunction' in self.urls:
self.friends += [('L-function', self.urls['Lfunction'])]
else:
self.friends += [('L-function not available', "")]
self.properties = [('Base field', self.field_name),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)
]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label, self.urls['class'])]
def random_curve():
from sage.misc.prandom import randint
n = get_stats().counts()['ncurves']
n = randint(0,n-1)
E = db_ecnf().find()[n]
return redirect(url_for(".show_ecnf", nf=E['field_label'], conductor_label=E['conductor_label'], class_label=E['iso_label'], number=E['number']), 301)
def elliptic_curve_search(**args):
info = to_dict(args["data"])
if "jump" in info:
label = info.get("label", "").replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
label_parts = label.split("-", 2)
nf = label_parts[0]
cond_label = label_parts[1]
cur_label = label_parts[2]
return show_ecnf(nf, cond_label, cur_label) ##!!!
query = {}
if "conductor_norm" in info:
Nnorm = clean_input(info["conductor_norm"])
Nnorm = Nnorm.replace("..", "-").replace(" ", "")
tmp = parse_range2(Nnorm, "conductor_norm")
if tmp[0] == "$or" and "$or" in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query["$or"]]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if "conductor_label" in info:
query["conductor_label"] = info["conductor_label"]
if "include_isogenous" in info and info["include_isogenous"] == "off":
query["number"] = 1
if "field" in info:
query["field_label"] = info["field"]
info["query"] = query
# process count and start if not default:
count_default = 50
if info.get("count"):
try:
count = int(info["count"])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get("start"):
try:
start = int(info["start"])
if start < 0:
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort(
[
("field_label", ASC),
("conductor_norm", ASC),
("conductor_label", ASC),
("iso_label", ASC),
("number", ASC),
]
)
.skip(start)
.limit(count)
)
bread = [("Elliptic Curves", url_for(".index")), ("Search Results", ".")]
res = list(res)
for e in res:
e["numb"] = str(e["number"])
e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), e["field_label"])
info["curves"] = res # [ECNF(e) for e in res]
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
info["field_pretty"] = field_pretty
info["web_ainvs"] = web_ainvs
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
t = "Elliptic Curve search results"
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
label_parts = label.split("-",1)
nf = label_parts[0]
label = label_parts[1]
return show_ecnf(nf,label)
query = {}
if 'conductor_norm' in info:
Nnorm = clean_input(info['conductor_norm'])
Nnorm = Nnorm.replace('..', '-').replace(' ', '')
tmp = parse_range2(Nnorm, 'conductor_norm')
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
query['number'] = 1
if 'field' in info:
query['field_label'] = info['field']
info['query'] = query
# process count and start if not default:
count_default = 20
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if(start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_label', ASC), ('number', ASC)]).skip(start).limit(count)
bread = []#[('Elliptic Curves over Number Fields', url_for(".elliptic_curve_search")), ]
bread = [('Elliptic Curves', url_for(".index")),
('Search Results', '.')]
res = list(res)
for e in res:
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), e['field_label'])
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args):
info = to_dict(args["data"])
if "jump" in info:
label = info.get("label", "").replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label)
except IndexError:
if not "query" in info:
info["query"] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info["err"] = "No elliptic curve in the database has label %s." % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [("Elliptic Curves", url_for(".index")), ("Search Results", ".")]
if "conductor_norm" in info:
Nnorm = clean_input(info["conductor_norm"])
Nnorm = Nnorm.replace("..", "-").replace(" ", "")
tmp = parse_range2(Nnorm, "conductor_norm")
if tmp[0] == "$or" and "$or" in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query["$or"]]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if "conductor_label" in info:
query["conductor_label"] = info["conductor_label"]
if "jinv" in info:
query["jinv"] = info["jinv"]
if info.get("torsion"):
ran = info["torsion"] = clean_input(info["torsion"])
ran = ran.replace("..", "-").replace(" ", "")
if not LIST_RE.match(ran):
info[
"err"
] = "Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121)."
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, "torsion_order")
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == "$or" and "$or" in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query["$or"]]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if "torsion_structure" in info and info["torsion_structure"]:
res = parse_torsion_structure(info["torsion_structure"], 2)
if "Error" in res:
info["err"] = res
return search_input_error(info, bread)
# update info for repeat searches
info["torsion_structure"] = str(res).replace(" ", "")
query["torsion_structure"] = [int(r) for r in res]
if "include_isogenous" in info and info["include_isogenous"] == "off":
query["number"] = 1
if "include_base_change" in info and info["include_base_change"] == "off":
query["base_change"] = []
else:
info["include_base_change"] = "on"
if "field" in info:
query["field_label"] = parse_field_string(info["field"])
info["query"] = query
# process count and start if not default:
count_default = 50
if info.get("count"):
try:
count = int(info["count"])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get("start"):
try:
start = int(info["start"])
if start < 0:
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if start >= nres:
start -= (1 + (start - nres) / count) * count
if start < 0:
start = 0
res = (
cursor.sort(
[
("field_label", ASC),
("conductor_norm", ASC),
("conductor_label", ASC),
("iso_label", ASC),
("number", ASC),
]
)
.skip(start)
.limit(count)
)
res = list(res)
for e in res:
e["numb"] = str(e["number"])
e["field_knowl"] = nf_display_knowl(e["field_label"], getDBConnection(), e["field_label"])
info["curves"] = res # [ECNF(e) for e in res]
info["number"] = nres
info["start"] = start
info["count"] = count
info["more"] = int(start + count < nres)
info["field_pretty"] = field_pretty
info["web_ainvs"] = web_ainvs
if nres == 1:
info["report"] = "unique match"
else:
if nres > count or start != 0:
info["report"] = "displaying matches %s-%s of %s" % (start + 1, min(nres, start + count), nres)
else:
info["report"] = "displaying all %s matches" % nres
t = "Elliptic Curve search results"
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(info):
if info.get('download') == '1' and info.get('Submit') and info.get(
'query'):
return download_search(info)
if not 'query' in info:
info['query'] = {}
bread = info.get('bread', [('Elliptic Curves', url_for(".index")),
('Search Results', '.')])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except ValueError:
info['err'] = ''
return search_input_error(info, bread)
return redirect(
url_for(".show_ecnf",
nf=nf,
conductor_label=cond_label,
class_label=iso_label,
number=number), 301)
query = {}
if 'jinv' in info:
if info.get('field', '').strip() == '2.2.5.1':
info['jinv'] = info['jinv'].replace('phi', 'a')
if info.get('field', '').strip() == '2.0.4.1':
info['jinv'] = info['jinv'].replace('i', 'a')
try:
parse_ints(info, query, 'conductor_norm')
parse_noop(info, query, 'conductor_label')
parse_nf_string(info,
query,
'field',
name="base number field",
qfield='field_label')
parse_nf_elt(info, query, 'jinv', name='j-invariant')
parse_ints(info,
query,
'torsion',
name='Torsion order',
qfield='torsion_order')
parse_bracketed_posints(info, query, 'torsion_structure', maxlength=2)
if 'torsion_structure' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(
mul, [int(n) for n in query['torsion_structure']], 1)
parse_ints(info, query, field='isodeg', qfield='isogeny_degrees')
except (TypeError, ValueError):
return search_input_error(info, bread)
if query.get('jinv'):
query['jinv'] = ','.join(query['jinv'])
if query.get('field_label') == '1.1.1.1':
return redirect(url_for("ec.rational_elliptic_curves", **request.args),
301)
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne': 0}
info['query'] = query
count = parse_count(info, 50)
start = parse_start(info)
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC),
('conductor_label', ASC), ('iso_nlabel', ASC),
('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'],
getDBConnection(),
field_pretty(e['field_label']))
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = info.get('title', 'Elliptic Curve search results')
return render_template("ecnf-search-results.html",
info=info,
credit=ecnf_credit,
bread=bread,
title=t)
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash(Markup("Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a" % args['label']), "error")
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
if hmf_field['narrow_class_no'] == 1 and nf.disc()**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [("Modular Forms", url_for('mf.modular_form_main_page')), ('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = db_forms().find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']},{'dimension':True})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': add_space_if_positive(teXify_pol(eigs[i])),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))
if not AL_eigs: # empty list
if data['level_norm']==1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len<=300)
info['display_eigs'] = display_eigs
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']),
('CM', is_CM),
('Base change', is_base_change)
]
return render_template("hilbert_modular_form.html", downloads=info["downloads"], info=info, properties2=properties2, credit=hmf_credit, title=t, bread=bread, friends=info['friends'], learnmore=learnmore_list())
def render_hmf_webpage(**args):
C = getDBConnection()
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such form"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [('Download to Magma',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='magma')),
('Download to Sage',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='sage'))]
if hmf_field['narrow_class_no'] == 1 and nf.disc(
)**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'],
url_for("ecnf.show_ecnf_isoclass",
nf=lab[0],
conductor_label=lab[1],
class_label=lab[2]))]
bread = [('Hilbert Modular Forms',
url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = C.hmfs.forms.find({
'field_label': data['field_label'],
'level_ideal': data['level_ideal']
})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
w = polygen(QQ, 'w')
e = polygen(QQ, 'e')
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{
'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]
} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{
'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]
} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len <= 300)
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
for eig in info['AL_eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']), ('CM', is_CM),
('Base change', is_base_change)]
return render_template("hilbert_modular_form.html",
downloads=info["downloads"],
info=info,
properties2=properties2,
credit=hmf_credit,
title=t,
bread=bread,
friends=info['friends'],
learnmore=learnmore_list())
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [
c for c in db_ecnf().find({
'field_label': self.field_label,
'conductor_norm': self.conductor_norm,
'conductor_label': self.conductor_label,
'iso_nlabel': self.iso_nlabel
}).sort('number')
]
# Rank or bounds
try:
self.rk = web_latex(self.db_curves[0]['rank'])
except KeyError:
self.rk = "?"
try:
self.rk_bnds = "%s...%s" % tuple(self.db_curves[0]['rank_bounds'])
except KeyError:
self.rank_bounds = [0, sage.rings.infinity.Infinity]
self.rk_bnds = "not recorded"
# Extract the isogeny degree matrix from the database if possible, else create it
if hasattr(self, 'isogeny_matrix'):
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
else:
self.isogeny_matrix = make_iso_matrix(self.db_curves)
# Create isogeny graph:
self.graph = make_graph(self.isogeny_matrix)
P = self.graph.plot(edge_labels=True)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
self.field = field_pretty(self.field_label)
self.field_knowl = nf_display_knowl(self.field_label,
lmfdb.base.getDBConnection(),
self.field)
def curve_url(c):
return url_for(".show_ecnf",
nf=c['field_label'],
conductor_label=c['conductor_label'],
class_label=c['iso_label'],
number=c['number'])
self.curves = [[
c['short_label'],
curve_url(c),
web_ainvs(self.field_label, c['ainvs'])
] for c in self.db_curves]
self.urls = {}
self.urls['class'] = url_for(".show_ecnf_isoclass",
nf=self.field_label,
conductor_label=self.conductor_label,
class_label=self.iso_label)
self.urls['conductor'] = url_for(".show_ecnf_conductor",
nf=self.field_label,
conductor_label=self.conductor_label)
self.urls['field'] = url_for('.show_ecnf1', nf=self.field_label)
sig = self.signature
totally_real = sig[1] == 0
imag_quadratic = sig == [0, 1]
if totally_real:
self.hmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.urls['hmf'] = url_for('hmf.render_hmf_webpage',
field_label=self.field_label,
label=self.hmf_label)
self.urls['Lfunction'] = url_for("l_functions.l_function_hmf_page",
field=self.field_label,
label=self.hmf_label,
character='0',
number='0')
if imag_quadratic:
self.bmf_label = "-".join(
[self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if totally_real:
self.friends += [('Hilbert Modular Form ' + self.hmf_label,
self.urls['hmf'])]
self.friends += [('L-function', self.urls['Lfunction'])]
if imag_quadratic:
self.friends += [
('Bianchi Modular Form %s not available' % self.bmf_label, '')
]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)]
if self.rk != '?':
self.properties += [('Rank', '%s' % self.rk)]
else:
if self.rk_bnds == 'not recorded':
self.properties += [('Rank', '%s' % self.rk_bnds)]
else:
self.properties += [('Rank bounds', '%s' % self.rk_bnds)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.field_label, self.urls['field']),
(self.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.short_label,
self.urls['class'])]
def random_curve():
E = random_object_from_collection(db_ecnf())
return redirect(url_for(".show_ecnf", nf=E['field_label'], conductor_label=E['conductor_label'], class_label=E['iso_label'], number=E['number']), 301)
def render_hmf_webpage(**args):
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = get_hmf(label)
if data is None:
flash(
Markup(
"Error: <span style='color:black'>%s</span> is not a valid Hilbert modular form label. It must be of the form (number field label) - (level label) - (orbit label) separated by dashes, such as 2.2.5.1-31.1-a"
% args['label']), "error")
return search_input_error()
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
hmf_field = get_hmf_field(data['field_label'])
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['hmf_field'] = hmf_field
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [('Download to Magma',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='magma')),
('Download to Sage',
url_for(".render_hmf_webpage_download",
field_label=info['field_label'],
label=info['label'],
download_type='sage'))]
if hmf_field['narrow_class_no'] == 1 and nf.disc(
)**2 * data['level_norm'] < 40000:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page",
field=info['field_label'],
label=info['label'],
character='0',
number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'],
url_for("ecnf.show_ecnf_isoclass",
nf=lab[0],
conductor_label=lab[1],
class_label=lab[2]))]
bread = [('Hilbert Modular Forms',
url_for(".hilbert_modular_form_render_webpage")),
('%s' % data['label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = db_search().find(
{
'field_label': data['field_label'],
'level_ideal': data['level_ideal']
}, {'dimension': True})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
# Get hecke_polynomial, hecke_eigenvalues and AL_eigenvalues
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
info['numeigs'] = numeigs
hecke_pol = data['hecke_polynomial']
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
AL_eigs = data['AL_eigenvalues']
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{
'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]
} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = web_latex_split_on_pm(teXify_pol(hecke_pol))
if not AL_eigs: # empty list
if data['level_norm'] == 1: # OK, no bad primes
info['AL_eigs'] = 'none'
else: # not OK, AL eigs are missing
info['AL_eigs'] = 'missing'
else:
info['AL_eigs'] = [{
'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]
} for al in data['AL_eigenvalues']]
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len <= 300)
info['display_eigs'] = display_eigs
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label']),
('Dimension', '%s' % data['dimension']), ('CM', is_CM),
('Base change', is_base_change)]
return render_template("hilbert_modular_form.html",
downloads=info["downloads"],
info=info,
properties2=properties2,
credit=hmf_credit,
title=t,
bread=bread,
friends=info['friends'],
learnmore=learnmore_list())
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'download' in info and info['download'] != 0:
return download_search(info)
if not 'query' in info:
info['query'] = {}
bread = [('Elliptic Curves', url_for(".index")),
('Search Results', '.')]
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except ValueError:
info['err'] = ''
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
try:
parse_ints(info,query,'conductor_norm')
parse_noop(info,query,'conductor_label')
parse_nf_string(info,query,'field',name="base number field",qfield='field_label')
parse_nf_elt(info,query,'jinv',name='j-invariant')
parse_ints(info,query,'torsion',name='Torsion order',qfield='torsion_order')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2)
if 'torsion_structure' in query and not 'torsion_order' in query:
query['torsion_order'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
except ValueError:
return search_input_error(info, bread)
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
if 'include_Q_curves' in info:
if info['include_Q_curves'] == 'exclude':
query['q_curve'] = False
elif info['include_Q_curves'] == 'only':
query['q_curve'] = True
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
info['query'] = query
count = parse_count(info, 50)
start = parse_start(info)
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), field_pretty(e['field_label']))
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except IndexError:
if not 'query' in info:
info['query'] = {}
bread = [("Elliptic Curves", url_for(".index"))]
info[
'err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
bread = [('Elliptic Curves', url_for(".index")), ('Search Results', '.')]
if 'conductor_norm' in info:
Nnorm = clean_input(info['conductor_norm'])
Nnorm = Nnorm.replace('..', '-').replace(' ', '')
tmp = parse_range2(Nnorm, 'conductor_norm')
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'conductor_label' in info:
query['conductor_label'] = info['conductor_label']
if 'jinv' in info:
query['jinv'] = info['jinv']
if info.get('torsion'):
ran = info['torsion'] = clean_input(info['torsion'])
ran = ran.replace('..', '-').replace(' ', '')
if not LIST_RE.match(ran):
info[
'err'] = 'Error parsing input for the torsion order. It needs to be an integer (such as 5), a range of integers (such as 2-10 or 2..10), or a comma-separated list of these (such as 4,9,16 or 4-25, 81-121).'
return search_input_error(info, bread)
# Past input check
tmp = parse_range2(ran, 'torsion_order')
# work around syntax for $or
# we have to foil out multiple or conditions
if tmp[0] == '$or' and '$or' in query:
newors = []
for y in tmp[1]:
oldors = [dict.copy(x) for x in query['$or']]
for x in oldors:
x.update(y)
newors.extend(oldors)
tmp[1] = newors
query[tmp[0]] = tmp[1]
if 'torsion_structure' in info and info['torsion_structure']:
res = parse_torsion_structure(info['torsion_structure'], 2)
if 'Error' in res:
info['err'] = res
return search_input_error(info, bread)
#update info for repeat searches
info['torsion_structure'] = str(res).replace(' ', '')
query['torsion_structure'] = [int(r) for r in res]
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
if 'field' in info:
query['field_label'] = parse_field_string(info['field'])
info['query'] = query
# process count and start if not default:
count_default = 50
if info.get('count'):
try:
count = int(info['count'])
except:
count = count_default
else:
count = count_default
start_default = 0
if info.get('start'):
try:
start = int(info['start'])
if (start < 0):
start += (1 - (start + 1) / count) * count
except:
start = start_default
else:
start = start_default
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if (start >= nres):
start -= (1 + (start - nres) / count) * count
if (start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC),
('conductor_label', ASC), ('iso_nlabel', ASC),
('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'],
getDBConnection(),
e['field_label'])
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (
start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html",
info=info,
credit=ecnf_credit,
bread=bread,
title=t)
def render_hmf_webpage(**args):
C = getDBConnection()
if 'data' in args:
data = args['data']
label = data['label']
else:
label = str(args['label'])
data = C.hmfs.forms.find_one({'label': label})
if data is None:
return "No such form"
info = {}
try:
info['count'] = args['count']
except KeyError:
info['count'] = 10
try:
numeigs = request.args['numeigs']
numeigs = int(numeigs)
except:
numeigs = 20
hmf_field = C.hmfs.fields.find_one({'label': data['field_label']})
gen_name = findvar(hmf_field['ideals'])
nf = WebNumberField(data['field_label'], gen_name=gen_name)
info['field'] = nf
info['base_galois_group'] = nf.galois_string()
info['field_degree'] = nf.degree()
info['field_disc'] = str(nf.disc())
info['field_poly'] = teXify_pol(str(nf.poly()))
info.update(data)
info['downloads'] = [
('Download to Magma', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='magma')),
('Download to Sage', url_for(".render_hmf_webpage_download", field_label=info['field_label'], label=info['label'], download_type='sage'))
]
if hmf_field['narrow_class_no'] == 1:
info['friends'] = [('L-function',
url_for("l_functions.l_function_hmf_page", field=info['field_label'], label=info['label'], character='0', number='0'))]
else:
info['friends'] = [('L-function not available', "")]
if data['dimension'] == 1: # Try to attach associated elliptic curve
lab = split_class_label(info['label'])
ec_from_hmf = db_ecnf().find_one({"label": label + '1'})
if ec_from_hmf == None:
info['friends'] += [('Elliptic curve not available', "")]
else:
info['friends'] += [('Isogeny class ' + info['label'], url_for("ecnf.show_ecnf_isoclass", nf=lab[0], conductor_label=lab[1], class_label=lab[2]))]
bread = [('Hilbert Modular Forms', url_for(".hilbert_modular_form_render_webpage")), ('%s' % data[
'label'], ' ')]
t = "Hilbert Cusp Form %s" % info['label']
forms_space = C.hmfs.forms.find(
{'field_label': data['field_label'], 'level_ideal': data['level_ideal']})
dim_space = 0
for v in forms_space:
dim_space += v['dimension']
info['newspace_dimension'] = dim_space
w = polygen(QQ, 'w')
e = polygen(QQ, 'e')
eigs = data['hecke_eigenvalues']
eigs = eigs[:min(len(eigs), numeigs)]
primes = hmf_field['primes']
n = min(len(eigs), len(primes))
info['eigs'] = [{'eigenvalue': teXify_pol(eigs[i]),
'prime_ideal': teXify_pol(primes[i]),
'prime_norm': primes[i][1:primes[i].index(',')]} for i in range(n)]
try:
display_eigs = request.args['display_eigs']
if display_eigs in ['True', 'true', '1', 'yes']:
display_eigs = True
else:
display_eigs = False
except KeyError:
display_eigs = False
if 'numeigs' in request.args:
display_eigs = True
info['hecke_polynomial'] = teXify_pol(info['hecke_polynomial'])
if 'AL_eigenvalues_fixed' in data:
if data['AL_eigenvalues_fixed'] == 'done':
info['AL_eigs'] = [{'eigenvalue': teXify_pol(al[1]),
'prime_ideal': teXify_pol(al[0]),
'prime_norm': al[0][1:al[0].index(',')]} for al in data['AL_eigenvalues']]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
else:
info['AL_eigs'] = [{'eigenvalue': '?', 'prime_ideal': '?'}]
info['AL_eigs_count'] = len(info['AL_eigs']) != 0
max_eig_len = max([len(eig['eigenvalue']) for eig in info['eigs']])
display_eigs = display_eigs or (max_eig_len<=300)
if not display_eigs:
for eig in info['eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
for eig in info['AL_eigs']:
if len(eig['eigenvalue']) > 300:
eig['eigenvalue'] = '...'
info['level_ideal'] = teXify_pol(info['level_ideal'])
if 'is_CM' in data:
is_CM = data['is_CM']
else:
is_CM = '?'
info['is_CM'] = is_CM
if 'is_base_change' in data:
is_base_change = data['is_base_change']
else:
is_base_change = '?'
info['is_base_change'] = is_base_change
if 'q_expansions' in data:
info['q_expansions'] = data['q_expansions']
properties2 = [('Base field', '%s' % info['field'].field_pretty()),
('Weight', '%s' % data['weight']),
('Level norm', '%s' % data['level_norm']),
('Level', '$' + teXify_pol(data['level_ideal']) + '$'),
('Label', '%s' % data['label_suffix']),
('Dimension', '%s' % data['dimension']),
('CM', is_CM),
('Base change', is_base_change)
]
return render_template("hilbert_modular_form.html", downloads=info["downloads"], info=info, properties2=properties2, credit=hmf_credit, title=t, bread=bread, friends=info['friends'], learnmore=learnmore_list())
def elliptic_curve_search(**args):
info = to_dict(args['data'])
if 'download' in info and info['download'] != 0:
return download_search(info)
bread = [('Elliptic Curves', url_for(".index")),
('Search Results', '.')]
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
# This label should be a full isogeny class label or a full
# curve label (including the field_label component)
try:
nf, cond_label, iso_label, number = split_full_label(label.strip())
except ValueError:
if not 'query' in info:
info['query'] = {}
info['err'] = ''
return search_input_error(info, bread)
return show_ecnf(nf, cond_label, iso_label, number)
query = {}
try:
parse_ints(info,query,'conductor_norm')
parse_noop(info,query,'conductor_label')
parse_nf_string(info,query,'field',name="base number field",qfield='field_label')
parse_nf_elt(info,query,'jinv',name='j-invariant')
parse_ints(info,query,'torsion',name='Torsion order',qfield='torsion_order')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2)
except ValueError:
return search_input_error(info, bread)
if 'include_isogenous' in info and info['include_isogenous'] == 'off':
info['number'] = 1
query['number'] = 1
if 'include_base_change' in info and info['include_base_change'] == 'off':
query['base_change'] = []
else:
info['include_base_change'] = "on"
info['query'] = query
count = parse_count(info, 50)
start = parse_start(info)
# make the query and trim results according to start/count:
cursor = db_ecnf().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('field_label', ASC), ('conductor_norm', ASC), ('conductor_label', ASC), ('iso_nlabel', ASC), ('number', ASC)]).skip(start).limit(count)
res = list(res)
for e in res:
e['numb'] = str(e['number'])
e['field_knowl'] = nf_display_knowl(e['field_label'], getDBConnection(), field_pretty(e['field_label']))
info['curves'] = res # [ECNF(e) for e in res]
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
info['field_pretty'] = field_pretty
info['web_ainvs'] = web_ainvs
if nres == 1:
info['report'] = 'unique match'
else:
if nres > count or start != 0:
info['report'] = 'displaying matches %s-%s of %s' % (start + 1, min(nres, start + count), nres)
else:
info['report'] = 'displaying all %s matches' % nres
t = 'Elliptic Curve search results'
return render_template("ecnf-search-results.html", info=info, credit=ecnf_credit, bread=bread, title=t)
