def todays_curve():
from datetime import date
mordells_birthday = date(1888,1,28)
n = (date.today()-mordells_birthday).days
label = db_ec().find({'number' : int(1)})[n]['label']
#return render_curve_webpage_by_label(label)
return redirect(url_for(".by_ec_label", label=label), 307)
def todays_curve():
from datetime import date
mordells_birthday = date(1888,1,28)
n = (date.today()-mordells_birthday).days
label = db_ec().find({'number' : int(1)})[n]['label']
#return render_curve_webpage_by_label(label)
return redirect(url_for(".by_ec_label", label=label), 307)
def download_EC_all(label):
try:
N, iso, number = split_lmfdb_label(label)
except (ValueError,AttributeError):
return elliptic_curve_jump_error(label, {})
CDB = db_ec()
if number:
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
data_list = [data]
else:
data_list = sorted(list(CDB.find({'lmfdb_iso': label})), key=lambda E: E['number'])
if len(data_list) == 0:
return elliptic_curve_jump_error(label, {})
# For each curve we will output all data fields except the '_id':
# (This should also be possible by adding projection={'_id':False}
# to the find() call but on testing that timed out.)
for data in data_list:
data.pop('_id')
import json
response = make_response('\n\n'.join(json.dumps(d) for d in data_list))
response.headers['Content-type'] = 'text/plain'
return response
def download_EC_all(label):
try:
N, iso, number = split_lmfdb_label(label)
except (ValueError,AttributeError):
return elliptic_curve_jump_error(label, {})
CDB = db_ec()
if number:
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
data_list = [data]
else:
data_list = sorted(list(CDB.find({'lmfdb_iso': label})), key=lambda E: E['number'])
if len(data_list) == 0:
return elliptic_curve_jump_error(label, {})
# For each curve we will output all data fields except the '_id':
# (This should also be possible by adding projection={'_id':False}
# to the find() call but on testing that timed out.)
for data in data_list:
data.pop('_id')
import json
response = make_response('\n\n'.join(json.dumps(d) for d in data_list))
response.headers['Content-type'] = 'text/plain'
return response
def download_EC_qexp(label, limit):
CDB = db_ec()
N, iso, number = split_lmfdb_label(label)
if number:
data = CDB.find_one({'lmfdb_label': label})
else:
data = CDB.find_one({'lmfdb_iso': label})
E = EllipticCurve(parse_ainvs(data['ainvs']))
response = make_response(','.join(str(an) for an in E.anlist(int(limit), python_ints=True)))
response.headers['Content-type'] = 'text/plain'
return response
def download_EC_qexp(label, limit):
CDB = db_ec()
N, iso, number = split_lmfdb_label(label)
if number:
data = CDB.find_one({'lmfdb_label': label})
else:
data = CDB.find_one({'lmfdb_iso': label})
E = EllipticCurve(parse_ainvs(data['ainvs']))
response = make_response(','.join(str(an) for an in E.anlist(int(limit), python_ints=True)))
response.headers['Content-type'] = 'text/plain'
return response
def by_weierstrass(eqn):
w = weierstrass_eqn_regex.match(eqn)
if not w:
w = short_weierstrass_eqn_regex.match(eqn)
if not w:
return elliptic_curve_jump_error(eqn, {})
try:
ainvs = [ZZ(ai) for ai in w.groups()]
except TypeError:
return elliptic_curve_jump_error(eqn, {})
E = EllipticCurve(ainvs).global_minimal_model()
N = E.conductor()
ainvs = [str(ai) for ai in E.ainvs()]
xainvs = ''.join(['[',','.join(ainvs),']'])
data = db_ec().find_one({'xainvs': xainvs})
if data is None:
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
return elliptic_curve_jump_error(eqn, {'conductor':N}, missing_curve=True)
return redirect(url_for(".by_ec_label", label=data['lmfdb_label']), 301)
def by_weierstrass(eqn):
w = weierstrass_eqn_regex.match(eqn)
if not w:
w = short_weierstrass_eqn_regex.match(eqn)
if not w:
return elliptic_curve_jump_error(eqn, {})
try:
ainvs = [ZZ(ai) for ai in w.groups()]
except TypeError:
return elliptic_curve_jump_error(eqn, {})
E = EllipticCurve(ainvs).global_minimal_model()
N = E.conductor()
ainvs = [str(ai) for ai in E.ainvs()]
xainvs = ''.join(['[',','.join(ainvs),']'])
data = db_ec().find_one({'xainvs': xainvs})
if data is None:
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
return elliptic_curve_jump_error(eqn, {'conductor':N}, missing_curve=True)
return redirect(url_for(".by_ec_label", label=data['lmfdb_label']), 301)
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 + ' [Weierstrass Coefficients]\n'
s += '\n' + com2
s += '\n'
if dltype == 'magma':
s += 'data := ['
else:
s += 'data = ['
s += '\\\n'
# reissue saved query here
res = db_ec().find(ast.literal_eval(info["query"]))
for f in res:
entry = str(f['ainvs'])
entry = entry.replace('u', '')
entry = entry.replace('\'', '')
s += 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 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 + ' [Weierstrass Coefficients]\n'
s += '\n' + com2
s += '\n'
if dltype == 'magma':
s += 'data := ['
else:
s += 'data = ['
s += '\\\n'
# reissue saved query here
res = db_ec().find(ast.literal_eval(info["query"]))
for f in res:
entry = str(f['ainvs'])
entry = entry.replace('u','')
entry = entry.replace('\'','')
s += 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 plot_ec(label):
CDB = db_ec()
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
E = EllipticCurve(parse_ainvs(data['xainvs']))
P = E.plot()
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def by_ec_label(label):
ec_logger.debug(label)
# First see if we have an LMFDB label of a curve or class:
try:
N, iso, number = split_lmfdb_label(label)
if number:
return redirect(
url_for(".by_triple_label",
conductor=N,
iso_label=iso,
number=number))
else:
return redirect(
url_for(".by_double_iso_label", conductor=N, iso_label=iso))
except AttributeError:
ec_logger.debug("%s not a valid lmfdb label, trying cremona")
# Next see if we have a Cremona label of a curve or class:
try:
N, iso, number = split_cremona_label(label)
except AttributeError:
ec_logger.debug(
"%s not a valid cremona label either, trying Weierstrass")
eqn = label.replace(" ", "")
if weierstrass_eqn_regex.match(
eqn) or short_weierstrass_eqn_regex.match(eqn):
return by_weierstrass(eqn)
else:
return elliptic_curve_jump_error(label, {})
if number: # it's a curve
label_type = 'label'
else:
label_type = 'iso'
data = db_ec().find_one({label_type: label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
iso = data['lmfdb_iso'].split(".")[1]
if number:
return redirect(
url_for(".by_triple_label",
conductor=N,
iso_label=iso,
number=data['lmfdb_number']))
else:
return redirect(
url_for(".by_double_iso_label", conductor=N, iso_label=iso))
def plot_ec(label):
CDB = db_ec()
data = CDB.find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
E = EllipticCurve(parse_ainvs(data['xainvs']))
P = E.plot()
_, filename = tempfile.mkstemp('.png')
P.save(filename)
data = open(filename).read()
os.unlink(filename)
response = make_response(data)
response.headers['Content-type'] = 'image/png'
return response
def isogeny_class_table(Nmin, Nmax):
''' Returns a table of all isogeny classes of elliptic curves with
conductor in the ranges NMin, NMax.
'''
iso_list = []
query = {'number': 1, 'conductor': {'$lte': Nmax, '$gte': Nmin}}
# Get all the curves and sort them according to conductor
cursor = db_ec().find(query,{'_id':False,'conductor':True,'lfmdb_label':True,'lmfdb_iso':True})
res = cursor.sort([('conductor', ASCENDING), ('lmfdb_label', ASCENDING)])
iso_list = [E['lmfdb_iso'].split('.') for E in res]
return iso_list
def by_label(label):
"""
Searches for a specific elliptic curve isogeny class in the
curves collection by its label, which can be either a curve
label (e.g. "11.a1") or a class label (e.g. "11.a") in either
LMFDB or Cremona format.
"""
try:
N, iso, number = split_lmfdb_label(label)
if number:
label = ".".join([N,iso])
data = db_ec().find_one({"lmfdb_iso" : label, 'number':1})
except AttributeError:
try:
N, iso, number = split_cremona_label(label)
if number:
label = "".join([N,iso])
data = db_ec().find_one({"iso" : label, 'number':1})
except AttributeError:
return "Invalid label" # caller must catch this and raise an error
if data:
return ECisog_class(data)
return "Class not found" # caller must catch this and raise an error
def isogeny_class_table(Nmin, Nmax):
''' Returns a table of all isogeny classes of elliptic curves with
conductor in the ranges NMin, NMax.
'''
iso_list = []
query = {'number': 1, 'conductor': {'$lte': Nmax, '$gte': Nmin}}
# Get all the curves and sort them according to conductor
cursor = db_ec().find(query,{'_id':False,'conductor':True,'lfmdb_label':True,'lmfdb_iso':True})
res = cursor.sort([('conductor', ASCENDING), ('lmfdb_label', ASCENDING)])
iso_list = [E['lmfdb_iso'] for E in res]
return iso_list
def modular_form_display(label, number):
try:
number = int(number)
except ValueError:
number = 10
if number < 10:
number = 10
if number > 1000:
number = 1000
data = db_ec().find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
E = EllipticCurve(parse_ainvs(data['xainvs']))
modform = E.q_eigenform(number)
modform_string = web_latex_split_on_pm(modform)
return modform_string
def modular_form_display(label, number):
try:
number = int(number)
except ValueError:
number = 10
if number < 10:
number = 10
if number > 1000:
number = 1000
data = db_ec().find_one({'lmfdb_label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
E = EllipticCurve(parse_ainvs(data['xainvs']))
modform = E.q_eigenform(number)
modform_string = web_latex_split_on_pm(modform)
return modform_string
def by_ec_label(label):
ec_logger.debug(label)
# First see if we have an LMFDB label of a curve or class:
try:
N, iso, number = split_lmfdb_label(label)
if number:
return redirect(url_for(".by_triple_label", conductor=N, iso_label=iso, number=number))
else:
return redirect(url_for(".by_double_iso_label", conductor=N, iso_label=iso))
except AttributeError:
ec_logger.debug("%s not a valid lmfdb label, trying cremona")
# Next see if we have a Cremona label of a curve or class:
try:
N, iso, number = split_cremona_label(label)
except AttributeError:
ec_logger.debug("%s not a valid cremona label either, trying Weierstrass")
eqn = label.replace(" ","")
if weierstrass_eqn_regex.match(eqn) or short_weierstrass_eqn_regex.match(eqn):
return by_weierstrass(eqn)
else:
return elliptic_curve_jump_error(label, {})
if number: # it's a curve
label_type = 'label'
else:
label_type = 'iso'
data = db_ec().find_one({label_type: label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
iso = data['lmfdb_iso'].split(".")[1]
if number:
return redirect(url_for(".by_triple_label", conductor=N, iso_label=iso, number=data['lmfdb_number']))
else:
return redirect(url_for(".by_double_iso_label", conductor=N, iso_label=iso))
def download_search(info):
dltype = info['Submit']
com = r'\\' # single line comment start
com1 = '' # multiline comment start
com2 = '' # multiline comment end
ass = '=' # assignment
eol = '' # end of line
filename = 'elliptic_curves.gp'
mydate = time.strftime("%d %B %Y")
if dltype == 'sage':
com = '#'
filename = 'elliptic_curves.sage'
if dltype == 'magma':
com = ''
com1 = '/*'
com2 = '*/'
ass = ":="
eol = ';'
filename = 'elliptic_curves.m'
s = com1 + "\n"
s += com + ' Elliptic curves downloaded from the LMFDB downloaded on {}.\n'.format(
mydate)
s += com + ' Below is a list called data. Each entry has the form:\n'
s += com + ' [a1,a2,a3,a4,a6] (Weierstrass Coefficients)\n'
s += '\n' + com2 + '\n'
s += 'data ' + ass + ' [' + '\\\n'
# reissue saved query here
res = db_ec().find(ast.literal_eval(info["query"]))
s += ",\\\n".join([str(f['xainvs']) for f in res])
s += ']' + eol + '\n'
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=filename,
as_attachment=True,
add_etags=False)
def download_search(info):
dltype = info['Submit']
com = r'\\' # single line comment start
com1 = '' # multiline comment start
com2 = '' # multiline comment end
ass = '=' # assignment
eol = '' # end of line
filename = 'elliptic_curves.gp'
mydate = time.strftime("%d %B %Y")
if dltype == 'sage':
com = '#'
filename = 'elliptic_curves.sage'
if dltype == 'magma':
com = ''
com1 = '/*'
com2 = '*/'
ass = ":="
eol = ';'
filename = 'elliptic_curves.m'
s = com1 + "\n"
s += com + ' Elliptic curves downloaded from the LMFDB downloaded on {}.\n'.format(mydate)
s += com + ' Below is a list called data. Each entry has the form:\n'
s += com + ' [a1,a2,a3,a4,a6] (Weierstrass Coefficients)\n'
s += '\n' + com2 + '\n'
s += 'data ' + ass + ' [' + '\\\n'
# reissue saved query here
res = db_ec().find(ast.literal_eval(info["query"]))
s += ",\\\n".join([str(f['xainvs']) for f in res])
s += ']' + eol + '\n'
strIO = StringIO.StringIO()
strIO.write(s)
strIO.seek(0)
return send_file(strIO,
attachment_filename=filename,
as_attachment=True,
add_etags=False)
def random_curve():
label = random_object_from_collection( db_ec() )['lmfdb_label']
cond, iso, num = split_lmfdb_label(label)
return redirect(url_for(".by_triple_label", conductor=cond, iso_label=iso, number=num))
def elliptic_curve_search(info):
if info.get('download') == '1' and info.get('Submit') and info.get('query'):
return download_search(info)
if 'SearchAgain' in info:
return rational_elliptic_curves()
query = {}
bread = info.get('bread',[('Elliptic Curves', url_for("ecnf.index")), ('$\Q$', url_for(".rational_elliptic_curves")), ('Search Results', '.')])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
xainvs = ''.join(['[',','.join(ainvs),']'])
data = db_ec().find_one({'xainvs': xainvs})
if data is None:
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
try:
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,process=str,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
if 'torsion_structure' in query and not 'torsion' in query:
query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='surjective primes',
qfield='non-maximal_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-surjective primes',
qfield='non-maximal_primes',mode=mode)
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info,100)
start = parse_start(info)
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['query'] = query
cursor = db_ec().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING),
('lmfdb_number', ASCENDING)]).skip(start).limit(count)
info['curves'] = res
info['format_ainvs'] = format_ainvs
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
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
#credit = 'John Cremona'
#if 'non-surjective_primes' in query or 'non-maximal_primes' in query:
# credit += ' and Andrew Sutherland'
t = info.get('title','Elliptic Curves search results')
return render_template("ec-search-results.html", info=info, credit=ec_credit(), bread=bread, title=t)
def random_curve():
label = random_object_from_collection( db_ec() )['lmfdb_label']
cond, iso, num = split_lmfdb_label(label)
return redirect(url_for(".by_triple_label", conductor=cond, iso_label=iso, number=num))
def isogeny_class_cm(label):
return db_ec().find_one({'lmfdb_iso': label}, {
'_id': False,
'cm': True
})['cm']
def make_class(self):
self.CM = self.cm
N, iso, number = split_lmfdb_label(self.lmfdb_iso)
# Extract the size of the isogeny class from the database
ncurves = self.class_size
# Create a list of the curves in the class from the database
self.curves = [db_ec().find_one({'iso':self.iso, 'lmfdb_number': i+1})
for i in range(ncurves)]
# Set optimality flags. The optimal curve is number 1 except
# in one case which is labeled differently in the Cremona tables
for c in self.curves:
c['optimal'] = (c['number']==(3 if self.label == '990h' else 1))
c['ai'] = parse_ainvs(c['xainvs'])
c['url'] = url_for(".by_triple_label", conductor=N, iso_label=iso, number=c['lmfdb_number'])
from sage.matrix.all import Matrix
self.isogeny_matrix = Matrix(self.isogeny_matrix)
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
# 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.newform = web_latex(PowerSeriesRing(QQ, 'q')(self.anlist, 20, check=True))
self.newform_label = newform_label(N,2,1,iso)
self.newform_link = url_for("emf.render_elliptic_modular_forms", level=N, weight=2, character=1, label=iso)
self.newform_exists_in_db = is_newform_in_db(self.newform_label)
self.lfunction_link = url_for("l_functions.l_function_ec_page", conductor_label = N, isogeny_class_label = iso)
self.friends = [('L-function', self.lfunction_link)]
if not self.CM:
self.CM = "no"
if int(N)<=300:
self.friends += [('Symmetric square L-function', url_for("l_functions.l_function_ec_sym_page", power='2', conductor = N, isogeny = iso))]
if int(N)<=50:
self.friends += [('Symmetric cube L-function', url_for("l_functions.l_function_ec_sym_page", power='3', conductor = N, isogeny = iso))]
if self.newform_exists_in_db:
self.friends += [('Modular form ' + self.newform_label, self.newform_link)]
self.properties = [('Label', self.lmfdb_iso),
('Number of curves', str(ncurves)),
('Conductor', '\(%s\)' % N),
('CM', '%s' % self.CM),
('Rank', '\(%s\)' % self.rank),
('Graph', ''),(None, self.graph_link)
]
self.downloads = [('Download coefficients of newform', url_for(".download_EC_qexp", label=self.lmfdb_iso, limit=1000)),
('Download stored data for all curves', url_for(".download_EC_all", label=self.lmfdb_iso))]
if self.lmfdb_iso == self.iso:
self.title = "Elliptic Curve Isogeny Class %s" % self.lmfdb_iso
else:
self.title = "Elliptic Curve Isogeny Class %s (Cremona label %s)" % (self.lmfdb_iso, self.iso)
self.bread = [('Elliptic Curves', url_for("ecnf.index")),
('$\Q$', url_for(".rational_elliptic_curves")),
('%s' % N, url_for(".by_conductor", conductor=N)),
('%s' % iso, ' ')]
self.code = {}
self.code['show'] = {'sage':''} # use default show names
self.code['class'] = {'sage':'E = EllipticCurve("%s1")\n'%(self.lmfdb_iso) + 'E.isogeny_class()\n'}
self.code['curves'] = {'sage':'E.isogeny_class().curves'}
self.code['rank'] = {'sage':'E.rank()'}
self.code['q_eigenform'] = {'sage':'E.q_eigenform(10)'}
self.code['matrix'] = {'sage':'E.isogeny_class().matrix()'}
self.code['plot'] = {'sage':'E.isogeny_graph().plot(edge_labels=True)'}
def nr_of_EC_in_isogeny_class(label):
''' Returns the number of elliptic curves in the isogeny class
with given label.
'''
return db_ec().find({'lmfdb_iso':label}).count()
def nr_of_EC_in_isogeny_class(label):
''' Returns the number of elliptic curves in the isogeny class
with given label.
'''
return db_ec().find({'lmfdb_iso': label}).count()
def isogeny_class_cm(label):
return db_ec().find_one({'lmfdb_iso':label},{'_id':False,'cm':True})['cm']
def __init__(self):
logger.debug("Constructing an instance of ECstats")
self.ecdb = db_ec()
self._counts = {}
self._stats = {}
def elliptic_curve_search(info):
if info.get('download') == '1' and info.get('Submit') and info.get('query'):
return download_search(info)
if 'SearchAgain' in info:
return rational_elliptic_curves()
query = {}
bread = info.get('bread',[('Elliptic Curves', url_for("ecnf.index")), ('$\Q$', url_for(".rational_elliptic_curves")), ('Search Results', '.')])
if 'jump' in info:
label = info.get('label', '').replace(" ", "")
m = match_lmfdb_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif label.startswith("Cremona:"):
label = label[8:]
m = match_cremona_label(label)
if m:
try:
return by_ec_label(label)
except ValueError:
return elliptic_curve_jump_error(label, info, wellformed_label=True)
elif match_cremona_label(label):
return elliptic_curve_jump_error(label, info, cremona_label=True)
elif label:
# Try to parse a string like [1,0,3,2,4] as valid
# Weistrass coefficients:
lab = re.sub(r'\s','',label)
lab = re.sub(r'^\[','',lab)
lab = re.sub(r']$','',lab)
try:
labvec = lab.split(',')
labvec = [QQ(str(z)) for z in labvec] # Rationals allowed
E = EllipticCurve(labvec)
# Now we do have a valid curve over Q, but it might
# not be in the database.
ainvs = [str(c) for c in E.minimal_model().ainvs()]
xainvs = ''.join(['[',','.join(ainvs),']'])
data = db_ec().find_one({'xainvs': xainvs})
if data is None:
data = db_ec().find_one({'ainvs': ainvs})
if data is None:
info['conductor'] = E.conductor()
return elliptic_curve_jump_error(label, info, missing_curve=True)
return by_ec_label(data['lmfdb_label'])
except (TypeError, ValueError, ArithmeticError):
return elliptic_curve_jump_error(label, info)
else:
query['label'] = ''
try:
parse_rational(info,query,'jinv','j-invariant')
parse_ints(info,query,'conductor')
parse_ints(info,query,'torsion','torsion order')
parse_ints(info,query,'rank')
parse_ints(info,query,'sha','analytic order of Ш')
parse_bracketed_posints(info,query,'torsion_structure',maxlength=2,process=str,check_divisibility='increasing')
# speed up slow torsion_structure searches by also setting torsion
if 'torsion_structure' in query and not 'torsion' in query:
query['torsion'] = reduce(mul,[int(n) for n in query['torsion_structure']],1)
if 'include_cm' in info:
if info['include_cm'] == 'exclude':
query['cm'] = 0
elif info['include_cm'] == 'only':
query['cm'] = {'$ne' : 0}
parse_ints(info,query,field='isodeg',qfield='isogeny_degrees')
parse_primes(info, query, 'surj_primes', name='surjective primes',
qfield='non-maximal_primes', mode='complement')
if info.get('surj_quantifier') == 'exactly':
mode = 'exact'
else:
mode = 'append'
parse_primes(info, query, 'nonsurj_primes', name='non-surjective primes',
qfield='non-maximal_primes',mode=mode)
except ValueError as err:
info['err'] = str(err)
return search_input_error(info, bread)
count = parse_count(info,100)
start = parse_start(info)
if 'optimal' in info and info['optimal'] == 'on':
# fails on 990h3
query['number'] = 1
info['query'] = query
cursor = db_ec().find(query)
nres = cursor.count()
if(start >= nres):
start -= (1 + (start - nres) / count) * count
if(start < 0):
start = 0
res = cursor.sort([('conductor', ASCENDING), ('iso_nlabel', ASCENDING),
('lmfdb_number', ASCENDING)]).skip(start).limit(count)
info['curves'] = res
info['format_ainvs'] = format_ainvs
info['curve_url'] = lambda dbc: url_for(".by_triple_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1], number=dbc['lmfdb_number'])
info['iso_url'] = lambda dbc: url_for(".by_double_iso_label", conductor=dbc['conductor'], iso_label=split_lmfdb_label(dbc['lmfdb_iso'])[1])
info['number'] = nres
info['start'] = start
info['count'] = count
info['more'] = int(start + count < nres)
if nres == 1:
info['report'] = 'unique match'
elif nres == 2:
info['report'] = 'displaying both matches'
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
credit = 'John Cremona'
if 'non-surjective_primes' in query or 'non-maximal_primes' in query:
credit += ' and Andrew Sutherland'
t = info.get('title','Elliptic Curves search results')
return render_template("ec-search-results.html", info=info, credit=credit, bread=bread, title=t)
def __init__(self):
logger.debug("Constructing an instance of ECstats")
self.ecdb = db_ec()
self._counts = {}
self._stats = {}
def getEllipticCurveData(label):
from lmfdb.elliptic_curves.web_ec import db_ec
return db_ec().find_one({'lmfdb_label': label})
