lambda field, conductor, iso, short_class_label: '<a href="%s">%s</a>'
% (url_for('.show_ecnf_isoclass',
nf=field,
conductor_label=conductor,
class_label=iso), short_class_label),
default=True,
align="center"),
MultiProcessedCol(
"ainvs", "ec.weierstrass_coeffs", "Weierstrass coefficients",
["field_label", "conductor_label", "iso_label", "number", "ainvs"],
lambda field, conductor, iso, number, ainvs: '<a href="%s">%s</a>' %
(url_for('.show_ecnf',
nf=field,
conductor_label=conductor,
class_label=iso,
number=number), web_ainvs(field, ainvs)))
])
ecnf_columns.above_results = """<p> *The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.</p>"""
@search_wrap(table=db.ec_nfcurves,
title='Elliptic curve search results',
err_title='Elliptic curve search input error',
columns=ecnf_columns,
shortcuts={
'jump': elliptic_curve_jump,
'download': download_search
},
def make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = list(db.ec_nfcurves.search(
{'field_label': self.field_label,
'conductor_norm': self.conductor_norm,
'conductor_label': self.conductor_label,
'iso_nlabel': self.iso_nlabel}))
# 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, 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 = list(db.ec_nfcurves.search(
{'field_label': self.field_label,
'conductor_norm': self.conductor_norm,
'conductor_label': self.conductor_label,
'iso_nlabel': self.iso_nlabel}))
# 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, 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)
lfun_url = url_for("l_functions.l_function_ecnf_page", field_label=self.field_label, conductor_label=self.conductor_label, isogeny_class_label=self.iso_label)
origin_url = lfun_url.lstrip('/L/').rstrip('/')
if sig[0] <= 2 and db.lfunc_instances.exists({'url': origin_url}):
self.urls['Lfunction'] = lfun_url
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)
lfun_url = url_for("l_functions.l_function_ecnf_page", field_label=self.field_label, conductor_label=self.conductor_label, isogeny_class_label=self.iso_label)
origin_url = lfun_url.lstrip('/L/').rstrip('/')
if db.lfunc_instances.exists({'url':origin_url}):
self.urls['Lfunction'] = lfun_url
# most of this code is repeated in WebEllipticCurve.py
# and should be refactored
self.friends = []
if totally_real and 'Lfunction' not in self.urls:
self.friends += [('Hilbert modular form ' + self.hmf_label, self.urls['hmf'])]
if imag_quadratic:
if "CM" in self.label:
self.friends += [('Bianchi modular form is not cuspidal', '')]
elif 'Lfunction' not in self.urls:
if db.bmf_forms.label_exists(self.bmf_label):
self.friends += [('Bianchi modular form %s' % self.bmf_label, self.bmf_url)]
else:
self.friends += [('(Bianchi modular form %s)' % self.bmf_label, '')]
if 'Lfunction' in self.urls:
Lfun = get_lfunction_by_url(self.urls['Lfunction'].lstrip('/L').rstrip('/'), projection=['degree', 'trace_hash', 'Lhash'])
instances = get_instances_by_Lhash_and_trace_hash(
Lfun['Lhash'],
Lfun['degree'],
Lfun.get('trace_hash'))
exclude={elt[1].rstrip('/').lstrip('/') for elt in self.friends
if elt[1]}
exclude.add(lfun_url.lstrip('/L/').rstrip('/'))
self.friends += names_and_urls(instances, exclude=exclude)
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, 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'])]
["field_label", "conductor_label"],
lambda field, conductor: '<a href="%s">%s</a>' %(
url_for('.show_ecnf_conductor', nf=field, conductor_label=conductor),
conductor),
default=True, align="center"),
MultiProcessedCol("iso_class", "ec.isogeny_class", "Isogeny class",
["field_label", "conductor_label", "iso_label", "short_class_label"],
lambda field, conductor, iso, short_class_label: '<a href="%s">%s</a>' % (
url_for('.show_ecnf_isoclass', nf=field, conductor_label=conductor, class_label=iso),
short_class_label),
default=True, align="center"),
MultiProcessedCol("ainvs", "ec.weierstrass_coeffs", "Weierstrass coefficients",
["field_label", "conductor_label", "iso_label", "number", "ainvs"],
lambda field, conductor, iso, number, ainvs: '<a href="%s">%s</a>' % (
url_for('.show_ecnf', nf=field, conductor_label=conductor, class_label=iso, number=number),
web_ainvs(field, ainvs)),
short_title="Weier. coeffs", default=True),
MathCol("rank", "ec.rank", "Rank", default=True),
ProcessedCol("torsion_structure", "ec.torsion_subgroup", "Torsion",
lambda tors: f"${tors}$" if tors else "trivial",
default=True, align="center")])
ecnf_columns.above_results = """<p> *The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.</p>"""
@search_wrap(table=db.ec_nfcurves,
title='Elliptic curve search results',
err_title='Elliptic curve search input error',
columns=ecnf_columns,
shortcuts={'jump':elliptic_curve_jump,
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 make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [c for c in db_ec().find(
{'field_label': self.field_label, 'conductor_label':
self.conductor_label, 'iso_label': self.iso_label}).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 make_class(self):
# Create a list of the curves in the class from the database
self.db_curves = [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.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)
real_quadratic = self.signature == [2,0]
imag_quadratic = self.signature == [0,1]
if 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 imag_quadratic:
self.bmf_label = "-".join([self.field_label, self.conductor_label, self.iso_label])
self.friends = []
if real_quadratic:
self.friends += [('Hilbert Modular Form ' + self.hmf_label, self.urls['hmf'])]
if imag_quadratic:
self.friends += [('Bianchi Modular Form %s not yet available' % self.bmf_label, '')]
self.properties = [('Base field', self.field),
('Label', self.class_label),
(None, self.graph_link),
('Conductor', '%s' % self.conductor_label)
]
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'])]
