def show_ecnf(nf, conductor_label, class_label, number):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {'query':{}}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
code = ec.code()
code['show'] = {'magma':'','pari':'','sage':''} # use default show names
info = {}
return render_template("show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
code = code,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list())
def show_ecnf(nf, conductor_label, class_label, number):
nf_label = parse_field_string(nf)
label = "".join(
["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {}
info['query'] = {}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (
ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
info = {}
return render_template(
"show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info)
def show_ecnf(nf, conductor_label, class_label, number):
nf_label = parse_field_string(nf)
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {}
info['query'] = {}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
info = {}
return render_template("show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info)
def show_ecnf(nf, conductor_label, class_label, number):
try:
nf_label = nf_string_to_label(nf)
except ValueError:
return search_input_error()
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {"query": {}}
info["err"] = "No elliptic curve in the database has label %s." % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls["field"]))
bread.append((ec.conductor_label, ec.urls["conductor"]))
bread.append((ec.iso_label, ec.urls["class"]))
bread.append((ec.number, ec.urls["curve"]))
info = {}
return render_template(
"show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list(),
)
def ecnf_code(**args):
label = "".join([
"-".join([args['nf'], args['conductor_label'], args['class_label']]),
args['number']
])
if not LABEL_RE.fullmatch(label):
return abort(404)
try:
E = ECNF.by_label(label)
except ValueError:
return abort(404)
Ecode = E.code()
lang = args['download_type']
code = "{} {} code for working with elliptic curve {}\n\n".format(
Comment[lang], Fullname[lang], label)
code += "{} (Note that not all these functions may be available, and some may take a long time to execute.)\n".format(
Comment[lang])
if lang == 'gp':
lang = 'pari'
for k in sorted_code_names:
if lang in Ecode[k]:
code += "\n{} {}: \n".format(Comment[lang], code_names[k])
code += Ecode[k][lang] + ('\n'
if not '\n' in Ecode[k][lang] else '')
return code
def show_ecnf(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])
ec = ECNF.by_label(label)
bread = [("Elliptic Curves", url_for(".index"))]
if not ec:
info = {'query':{}}
info['err'] = 'No elliptic curve in the database has label %s.' % label
return search_input_error(info, bread)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
code = ec.code()
code['show'] = {'magma':'','pari':'','sage':''} # use default show names
info = {}
return render_template("ecnf-curve.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
code = code,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
learnmore=learnmore_list())
def make_class(self):
self.ECNF = ECNF.by_label(self.label)
# Create a list of the curves in the class from the database
self.db_curves = [ECNF(c) for c in db_ec().find(
{'field_label' : self.field_label, 'conductor_label' :
self.conductor_label, 'iso_label' : self.iso_label}).sort('number')]
size = len(self.db_curves)
# 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.curves = [[c.short_label, c.urls['curve'], c.latex_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.ECNF.field_label)
self.field = self.ECNF.field
if self.field.is_real_quadratic():
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 self.field.is_imag_quadratic():
self.bmf_label = "-".join([self.field.label,self.conductor_label,self.iso_label])
self.friends = []
if self.field.is_real_quadratic():
self.friends += [('Hilbert Modular Form '+self.hmf_label, self.urls['hmf'])]
if self.field.is_imag_quadratic():
self.friends += [('Bianchi Modular Form %s not yet available' % self.bmf_label, '')]
self.properties = [('Label', self.ECNF.label),
(None, self.graph_link),
('Conductor', '%s' % self.ECNF.cond)
]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.ECNF.field_label, self.urls['field']),
(self.ECNF.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.ECNF.short_label, self.urls['class'])]
def ecnf_code(**args):
label = "".join(["-".join([args['nf'], args['conductor_label'], args['class_label']]), args['number']])
E = ECNF.by_label(label)
Ecode = E.code()
lang = args['download_type']
code = "{} {} code for working with elliptic curve {}\n\n".format(Comment[lang],Fullname[lang],label)
code += "{} (Note that not all these functions may be available, and some may take a long time to execute.)\n".format(Comment[lang])
if lang=='gp':
lang = 'pari'
for k in sorted_code_names:
if lang in Ecode[k]:
code += "\n{} {}: \n".format(Comment[lang],code_names[k])
code += Ecode[k][lang] + ('\n' if not '\n' in Ecode[k][lang] else '')
return code
def show_ecnf(nf, conductor_label, class_label, number):
if not FIELD_RE.fullmatch(nf):
return abort(404)
conductor_label = unquote(conductor_label)
conductor_label = convert_IQF_label(nf, conductor_label)
try:
nf_label = nf_string_to_label(nf)
except ValueError:
flash_error("%s is not a valid number field label", nf_label)
return redirect(url_for(".index"))
label = "".join(
["-".join([nf_label, conductor_label, class_label]),
str(number)])
if not LABEL_RE.fullmatch(label):
flash_error("%s is not a valid elliptic curve label", label)
return redirect(url_for(".index"))
ec = ECNF.by_label(label)
if not isinstance(ec, ECNF):
flash_error("There is no elliptic curve with label %s in the database",
label)
return redirect(url_for(".index"))
bread = [("Elliptic curves", url_for(".index"))]
title = "Elliptic curve %s over number field %s" % (
ec.short_label, ec.field.field_pretty())
bread = [("Elliptic curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls['field']))
bread.append((ec.conductor_label, ec.urls['conductor']))
bread.append((ec.iso_label, ec.urls['class']))
bread.append((ec.number, ec.urls['curve']))
code = ec.code()
code['show'] = {
'magma': '',
'pari': '',
'sage': ''
} # use default show names
info = {}
return render_template(
"ecnf-curve.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
code=code,
# properties = ec.properties,
properties=ec.properties,
friends=ec.friends,
downloads=ec.downloads,
info=info,
KNOWL_ID="ec.%s" % label,
learnmore=learnmore_list())
def show_ecnf(nf, label):
nf_label = parse_field_string(nf)
label = "-".join([nf_label, label])
ec = ECNF.by_label(label)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(),url_for(".show_ecnf1", nf=nf_label)))
bread.append((ec.short_label, url_for(".show_ecnf", label = ec.short_label, nf = nf_label)))
info = {}
return render_template("show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2 = ec.properties,
friends = ec.friends,
info=info)
def get_generators(field,
iso_class,
test_saturation=False,
verbose=False,
store=False):
r""" Retrieves the curves in the isogeny class from the database, finds
their ranks (or bounds) and generators, and optionally stores the
result back in the database. """
res = nfcurves.find({'field_label': field, 'short_class_label': iso_class})
if not res:
raise ValueError(
"No curves in the database ovver field %s in class %s" %
(field, iso_class))
Es = [ECNF(e).E for e in res]
if verbose:
print("Curves in class %s: %s" % (iso_class, [E.ainvs() for E in Es]))
mwi = MWInfo_curves(Es,
HeightBound=2,
test_saturation=test_saturation,
verbose=verbose)
if verbose:
print("MW info: %s" % mwi)
# res.rewind()
# We find the curves again, since the cursor times out after 10
# miniutes and finding the generators can take longer than that.
res = nfcurves.find({'field_label': field, 'short_class_label': iso_class})
for e, mw in zip(res, mwi):
data = {}
data['rank_bounds'] = [int(r) for r in mw[0]]
if mw[0][0] == mw[0][1]:
data['rank'] = int(mw[0][0])
data['gens'] = encode_points(mw[1])
if verbose:
print("About to update %s using data %s" % (e['label'], data))
if store:
nfcurves.update(e, {'$set': data}, upsert=True)
else:
if verbose:
print("(not done, dummy run)")
def show_ecnf(nf, class_label, conductor_label, number):
nf_label = parse_field_string(nf)
label = "".join(["-".join([nf_label, conductor_label, class_label]), number])
ec = ECNF.by_label(label)
title = "Elliptic Curve %s over Number Field %s" % (ec.short_label, ec.field.field_pretty())
bread = [("Elliptic Curves", url_for(".index"))]
bread.append((ec.field.field_pretty(), ec.urls["field"]))
bread.append((ec.conductor_label, ec.urls["conductor"]))
bread.append((ec.iso_label, ec.urls["class"]))
bread.append((ec.number, ec.urls["curve"]))
info = {}
return render_template(
"show-ecnf.html",
credit=ecnf_credit,
title=title,
bread=bread,
ec=ec,
# properties = ec.properties,
properties2=ec.properties,
friends=ec.friends,
info=info,
)
def ecnf_code(**args):
label = "".join([
"-".join([args['nf'], args['conductor_label'], args['class_label']]),
args['number']
])
E = ECNF.by_label(label)
Ecode = E.code()
lang = args['download_type']
code = "{} {} code for working with elliptic curve {}\n\n".format(
Comment[lang], Fullname[lang], label)
code += "{} (Note that not all these functions may be available, and some may take a long time to execute.)\n".format(
Comment[lang])
if lang == 'gp':
lang = 'pari'
if lang == 'sage':
code += "\nx = polygen(QQ)\n"
elif lang == 'magma':
code += "\nQx<x> := PolynomialRing(RationalField());\n"
for k in sorted_code_names:
if lang in Ecode[k]:
code += "\n{} {}: \n".format(Comment[lang], code_names[k])
code += Ecode[k][lang] + ('\n'
if not '\n' in Ecode[k][lang] else '')
return code
def make_class(self):
self.ECNF = ECNF.by_label(self.label)
# Create a list of the curves in the class from the database
self.db_curves = [
ECNF(c) for c in db_ec().find({
'field_label': self.field_label,
'conductor_label': self.conductor_label,
'iso_label': self.iso_label
}).sort('number')
]
size = len(self.db_curves)
# 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.curves = [[c.short_label, c.urls['curve'], c.latex_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.ECNF.field_label)
self.field = self.ECNF.field
if self.field.is_real_quadratic():
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 self.field.is_imag_quadratic():
self.bmf_label = "-".join(
[self.field.label, self.conductor_label, self.iso_label])
self.friends = []
if self.field.is_real_quadratic():
self.friends += [('Hilbert Modular Form ' + self.hmf_label,
self.urls['hmf'])]
if self.field.is_imag_quadratic():
self.friends += [
('Bianchi Modular Form %s not yet available' % self.bmf_label,
'')
]
self.properties = [('Label', self.ECNF.label), (None, self.graph_link),
('Conductor', '%s' % self.ECNF.cond)]
self.bread = [('Elliptic Curves ', url_for(".index")),
(self.ECNF.field_label, self.urls['field']),
(self.ECNF.conductor_label, self.urls['conductor']),
('isogeny class %s' % self.ECNF.short_label,
self.urls['class'])]
