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 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 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'])]
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)
# 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
real_quadratic = sig == [2, 0]
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)
# 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
real_quadratic = sig == [2,0]
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'])]
