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.
"""
#print "label = %s" % label
try:
N, iso, number = split_lmfdb_label(label)
if number:
data = db_ec().find_one({"lmfdb_label": label})
else:
data = db_ec().find_one({"lmfdb_label": label + "1"})
except AttributeError:
try:
N, iso, number = split_cremona_label(label)
if number:
data = db_ec().find_one({"label": label})
else:
data = db_ec().find_one({"label": label + "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 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_curves.lucky({"lmfdb_iso" : label, 'number':1})
data['label_type'] = 'LMFDB'
except AttributeError:
try:
N, iso, number = split_cremona_label(label)
if number:
label = "".join([N,iso])
data = db.ec_curves.lucky({"iso" : label, 'number':1})
data['label_type'] = 'Cremona'
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 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_curves.lucky({"lmfdb_iso": label, 'number': 1})
data['label_type'] = 'LMFDB'
except AttributeError:
try:
N, iso, number = split_cremona_label(label)
if number:
label = "".join([N, iso])
data = db.ec_curves.lucky({"iso": label, 'number': 1})
data['label_type'] = 'Cremona'
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 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.
"""
#print "label = %s" % label
try:
N, iso, number = split_lmfdb_label(label)
if number:
data = db_ec().find_one({"lmfdb_label" : label})
else:
data = db_ec().find_one({"lmfdb_label" : label+"1"})
except AttributeError:
try:
N, iso, number = split_cremona_label(label)
if number:
data = db_ec().find_one({"label" : label})
else:
data = db_ec().find_one({"label" : label+"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 by_ec_label(label):
ec_logger.debug(label)
try:
N, iso, number = split_lmfdb_label(label)
except AttributeError:
ec_logger.debug("%s not a valid lmfdb label, trying cremona")
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, {})
# We permanently redirect to the lmfdb label
if number:
data = db_ec().find_one({'label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
return redirect(url_for(".by_ec_label", label=data['lmfdb_label']), 301)
else:
data = db_ec().find_one({'iso': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
return redirect(url_for(".by_ec_label", label=data['lmfdb_iso']), 301)
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))
def url_for_ec(label):
if not '-' in label:
# Convert to LMFDB label on next run:
(conductor_label, class_label, number) = split_cremona_label(label)
return url_for('ecnf.show_ecnf', nf = 'Q', conductor_label =
conductor_label, class_label = class_label, number = number)
else:
(nf, conductor_label, class_label, number) = split_full_label(label)
return url_for('ecnf.show_ecnf', nf = nf, conductor_label =
conductor_label, class_label = class_label, number = number)
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 by_ec_label(label):
ec_logger.debug(label)
try:
N, iso, number = split_lmfdb_label(label)
except AttributeError:
ec_logger.debug("%s not a valid lmfdb label, trying cremona")
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, {})
# We permanently redirect to the lmfdb label
if number: # it's a curve
data = db_ec().find_one({'label': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
#return redirect(url_for(".by_ec_label", label=data['lmfdb_label']), 301)
return render_curve_webpage_by_label(data['label'])
else: # it's an isogeny class
data = db_ec().find_one({'iso': label})
if data is None:
return elliptic_curve_jump_error(label, {})
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
#return redirect(url_for(".by_ec_label", label=data['iso']), 301)
return render_isogeny_class(data['iso'])
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))
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_curves.lucky({label_type: label}, projection=1)
if data is None:
return elliptic_curve_jump_error(label, {}, wellformed_label=True, missing_curve=True)
ec_logger.debug(url_for(".by_ec_label", label=data['lmfdb_label']))
iso = data['lmfdb_iso'].split(".")[1]
if number:
return render_curve_webpage_by_label(label)
#return redirect(url_for(".by_triple_label", conductor=N, iso_label=iso, number=data['lmfdb_number']))
else:
return render_isogeny_class(label)
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
self.ncurves = ncurves = self.class_size
# Create a list of the curves in the class from the database
number_key = 'number' if self.label_type=='Cremona' else 'lmfdb_number'
self.curves = [db.ec_curves.lucky({'iso':self.iso, number_key: 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.iso == '990h' else 1))
c['ai'] = c['ainvs']
c['curve_url_lmfdb'] = url_for(".by_triple_label", conductor=N, iso_label=iso, number=c['lmfdb_number'])
c['curve_url_cremona'] = url_for(".by_ec_label", label=c['label'])
if self.label_type == 'Cremona':
c['curve_label'] = c['label']
_, c_iso, c_number = split_cremona_label(c['label'])
else:
c['curve_label'] = c['lmfdb_label']
_, c_iso, c_number = split_lmfdb_label(c['lmfdb_label'])
c['short_label'] = "{}{}".format(c_iso,c_number)
from sage.matrix.all import Matrix
if self.label_type == 'Cremona':
# permute rows/cols
perm = lambda i: (c for c in self.curves if c['number']==i+1).next()['lmfdb_number']-1
self.isogeny_matrix = [[self.isogeny_matrix[perm(i)][perm(j)] for i in range(ncurves)] for j in range(ncurves)]
self.isogeny_matrix = Matrix(self.isogeny_matrix)
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
# Create isogeny graph with appropriate vertex labels:
self.graph = make_graph(self.isogeny_matrix, [c['short_label'] for c in self.curves])
P = self.graph.plot(edge_labels=True, vertex_size=1000)
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 = db.mf_newforms.lucky({'level':N, 'weight':2, 'related_objects':{'$contains':'EllipticCurve/Q/%s/%s' % (N, iso)}},'label')
self.newform_exists_in_db = self.newform_label is not None
if self.newform_label is not None:
char_orbit, hecke_orbit = self.newform_label.split('.')[2:]
self.newform_link = url_for("cmf.by_url_newform_label", level=N, weight=2, char_orbit_label=char_orbit, hecke_orbit=hecke_orbit)
self.lfunction_link = url_for("l_functions.l_function_ec_page", conductor_label = N, isogeny_class_label = iso)
self.friends = [('L-function', self.lfunction_link)]
if not self.CM:
self.CM = "no"
if int(N)<=300:
self.friends += [('Symmetric square L-function', url_for("l_functions.l_function_ec_sym_page", power='2', conductor = N, isogeny = iso))]
if int(N)<=50:
self.friends += [('Symmetric cube L-function', url_for("l_functions.l_function_ec_sym_page", power='3', conductor = N, isogeny = iso))]
if self.newform_exists_in_db:
self.friends += [('Modular form ' + self.newform_label, self.newform_link)]
if self.label_type == 'Cremona':
self.title = "Elliptic Curve Isogeny Class with Cremona label {} (LMFDB label {})".format(self.iso, self.lmfdb_iso)
self.iso_label = self.iso
else:
self.title = "Elliptic Curve Isogeny Class with LMFDB label {} (Cremona label {})".format(self.lmfdb_iso, self.iso)
self.iso_label = self.lmfdb_iso
self.properties = [('Label', self.iso if self.label_type=='Cremona' else self.lmfdb_iso),
('Number of curves', str(ncurves)),
('Conductor', '%s' % N),
('CM', '%s' % self.CM),
('Rank', '%s' % self.rank)
]
if self.ncurves>1:
self.properties += [('Graph', ''),(None, self.graph_link)]
self.downloads = [('q-expansion to text', url_for(".download_EC_qexp", label=self.lmfdb_iso, limit=1000)),
('All stored data to text', url_for(".download_EC_all", label=self.lmfdb_iso))]
self.bread = [('Elliptic Curves', url_for("ecnf.index")),
('$\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 make_class(self):
self.CM = self.cm
N, iso, number = split_lmfdb_label(self.lmfdb_iso)
self.conductor = int(N)
# Extract the size of the isogeny class from the database
self.ncurves = ncurves = self.class_size
# Create a list of the curves in the class from the database
number_key = 'number' if self.label_type == 'Cremona' else 'lmfdb_number'
self.curves = [
db.ec_curves.lucky({
'iso': self.iso,
number_key: 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
self.optimality_known = (self.ncurves
== 1) or (self.conductor < OPTIMALITY_BOUND)
self.optimality_bound = OPTIMALITY_BOUND
for c in self.curves:
c['optimal'] = (c['number'] == (3 if self.iso == '990h' else 1))
c['ai'] = c['ainvs']
c['curve_url_lmfdb'] = url_for(".by_triple_label",
conductor=N,
iso_label=iso,
number=c['lmfdb_number'])
c['curve_url_cremona'] = url_for(".by_ec_label", label=c['label'])
if self.label_type == 'Cremona':
c['curve_label'] = c['label']
_, c_iso, c_number = split_cremona_label(c['label'])
else:
c['curve_label'] = c['lmfdb_label']
_, c_iso, c_number = split_lmfdb_label(c['lmfdb_label'])
c['short_label'] = "{}{}".format(c_iso, c_number)
from sage.matrix.all import Matrix
if self.label_type == 'Cremona':
# permute rows/cols
perm = lambda i: (c for c in self.curves if c['number'] == i + 1
).next()['lmfdb_number'] - 1
self.isogeny_matrix = [[
self.isogeny_matrix[perm(i)][perm(j)] for i in range(ncurves)
] for j in range(ncurves)]
self.isogeny_matrix = Matrix(self.isogeny_matrix)
self.isogeny_matrix_str = latex(matrix(self.isogeny_matrix))
# Create isogeny graph with appropriate vertex labels:
self.graph = make_graph(self.isogeny_matrix,
[c['short_label'] for c in self.curves])
P = self.graph.plot(edge_labels=True, vertex_size=1000)
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 = db.mf_newforms.lucky(
{
'level': N,
'weight': 2,
'related_objects': {
'$contains': 'EllipticCurve/Q/%s/%s' % (N, iso)
}
}, 'label')
self.newform_exists_in_db = self.newform_label is not None
if self.newform_label is not None:
char_orbit, hecke_orbit = self.newform_label.split('.')[2:]
self.newform_link = url_for("cmf.by_url_newform_label",
level=N,
weight=2,
char_orbit_label=char_orbit,
hecke_orbit=hecke_orbit)
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)]
if self.label_type == 'Cremona':
self.title = "Elliptic Curve Isogeny Class with Cremona label {} (LMFDB label {})".format(
self.iso, self.lmfdb_iso)
self.iso_label = self.iso
else:
self.title = "Elliptic Curve Isogeny Class with LMFDB label {} (Cremona label {})".format(
self.lmfdb_iso, self.iso)
self.iso_label = self.lmfdb_iso
self.properties = [
('Label',
self.iso if self.label_type == 'Cremona' else self.lmfdb_iso),
('Number of curves', str(ncurves)), ('Conductor', '%s' % N),
('CM', '%s' % self.CM), ('Rank', '%s' % self.rank)
]
if self.ncurves > 1:
self.properties += [('Graph', ''), (None, self.graph_link)]
self.downloads = [('q-expansion to text',
url_for(".download_EC_qexp",
label=self.lmfdb_iso,
limit=1000)),
('All stored data to text',
url_for(".download_EC_all", label=self.lmfdb_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 make_class(self):
# Extract the size of the isogeny class from the database
classdata = db.ec_classdata.lucky({'lmfdb_iso': self.lmfdb_iso})
self.class_size = ncurves = classdata['class_size']
# Create a list of the curves in the class from the database
number_key = 'Cnumber' if self.label_type == 'Cremona' else 'lmfdb_number'
self.curves = [
db.ec_curvedata.lucky({
'lmfdb_iso': self.lmfdb_iso,
number_key: i + 1
}) for i in range(ncurves)
]
# Set optimality flags. The optimal curve is conditionally
# number 1 except in one case which is labeled differently in
# the Cremona tables. We know which curve is optimal iff the
# optimality code for curve #1 is 1 (except for class 990h).
# Note that self is actually an elliptic curve, with number=1.
# The code here allows us to update the display correctly by
# changing one line in this file (defining OPTIMALITY_BOUND)
# without changing the data.
self.cremona_bound = CREMONA_BOUND
self.optimality_bound = OPTIMALITY_BOUND
self.optimality_known = (self.conductor < OPTIMALITY_BOUND) or (
(self.conductor < CREMONA_BOUND) and ((self.optimality == 1) or
(self.Ciso == '990h')))
self.optimal_label = self.Clabel if self.label_type == 'Cremona' else self.lmfdb_label
if self.conductor < OPTIMALITY_BOUND:
for c in self.curves:
c['optimal'] = (c['Cnumber'] == (3 if self.Ciso == '990h' else
1))
c['optimality_known'] = True
elif self.conductor < CREMONA_BOUND:
for c in self.curves:
c['optimal'] = (c['optimality'] > 0
) # this curve possibly optimal
c['optimality_known'] = (c['optimality'] == 1
) # this curve certainly optimal
else:
for c in self.curves:
c['optimal'] = None
c['optimality_known'] = False
for c in self.curves:
c['ai'] = c['ainvs']
c['curve_url_lmfdb'] = url_for(".by_triple_label",
conductor=self.conductor,
iso_label=self.iso_label,
number=c['lmfdb_number'])
c['curve_url_cremona'] = url_for(
".by_ec_label",
label=c['Clabel']) if self.conductor < CREMONA_BOUND else "N/A"
if self.label_type == 'Cremona':
c['curve_label'] = c['Clabel']
_, c_iso, c_number = split_cremona_label(c['Clabel'])
else:
c['curve_label'] = c['lmfdb_label']
_, c_iso, c_number = split_lmfdb_label(c['lmfdb_label'])
c['short_label'] = "{}{}".format(c_iso, c_number)
from sage.matrix.all import Matrix
M = classdata['isogeny_matrix']
# permute rows/cols to match labelling: the rows/cols in the
# ec_classdata table are with respect to LMFDB ordering.
if self.label_type == 'Cremona':
perm = lambda i: next(c for c in self.curves
if c['Cnumber'] == i + 1)['lmfdb_number'] - 1
M = [[M[perm(i)][perm(j)] for i in range(ncurves)]
for j in range(ncurves)]
M = Matrix(M)
self.isogeny_matrix_str = latex(M)
# Create isogeny graph with appropriate vertex labels:
self.graph = make_graph(M, [c['short_label'] for c in self.curves])
P = self.graph.plot(edge_labels=True, vertex_size=1000)
self.graph_img = encode_plot(P)
self.graph_link = '<img src="%s" width="200" height="150"/>' % self.graph_img
self.newform = raw_typeset(
PowerSeriesRing(QQ, 'q')(classdata['anlist'], 20, check=True))
self.newform_label = ".".join(
[str(self.conductor),
str(2), 'a', self.iso_label])
self.newform_exists_in_db = db.mf_newforms.label_exists(
self.newform_label)
if self.newform_exists_in_db:
char_orbit, hecke_orbit = self.newform_label.split('.')[2:]
self.newform_link = url_for("cmf.by_url_newform_label",
level=self.conductor,
weight=2,
char_orbit_label=char_orbit,
hecke_orbit=hecke_orbit)
self.lfunction_link = url_for("l_functions.l_function_ec_page",
conductor_label=self.conductor,
isogeny_class_label=self.iso_label)
self.friends = [('L-function', self.lfunction_link)]
if self.cm:
# set CM field for Properties box.
D = ZZ(self.cm).squarefree_part()
coeffs = [(1 - D) // 4, -1, 1] if D % 4 == 1 else [-D, 0, 1]
lab = db.nf_fields.lucky({'coeffs': coeffs}, projection='label')
self.CMfield = field_pretty(lab)
else:
self.CMfield = "no"
if self.conductor <= 300:
self.friends += [('Symmetric square L-function',
url_for("l_functions.l_function_ec_sym_page",
power='2',
conductor=self.conductor,
isogeny=self.iso_label))]
if self.conductor <= 50:
self.friends += [('Symmetric cube L-function',
url_for("l_functions.l_function_ec_sym_page",
power='3',
conductor=self.conductor,
isogeny=self.iso_label))]
if self.newform_exists_in_db:
self.friends += [('Modular form ' + self.newform_label,
self.newform_link)]
if self.label_type == 'Cremona':
self.title = "Elliptic curve isogeny class with Cremona label {} (LMFDB label {})".format(
self.Ciso, self.lmfdb_iso)
elif self.conductor < CREMONA_BOUND:
self.title = "Elliptic curve isogeny class with LMFDB label {} (Cremona label {})".format(
self.lmfdb_iso, self.Ciso)
else:
self.title = "Elliptic curve isogeny class with LMFDB label {}".format(
self.lmfdb_iso)
self.properties = [
('Label',
self.Ciso if self.label_type == 'Cremona' else self.lmfdb_iso),
('Number of curves', prop_int_pretty(ncurves)),
('Conductor', prop_int_pretty(self.conductor)),
('CM', '%s' % self.CMfield), ('Rank', prop_int_pretty(self.rank))
]
if ncurves > 1:
self.properties += [('Graph', ''), (None, self.graph_link)]
self.downloads = [('q-expansion to text',
url_for(".download_EC_qexp",
label=self.iso_label,
limit=1000)),
('All stored data to text',
url_for(".download_EC_all", label=self.iso_label))]
self.bread = [('Elliptic curves', url_for("ecnf.index")),
(r'$\Q$', url_for(".rational_elliptic_curves")),
('%s' % self.conductor,
url_for(".by_conductor", conductor=self.conductor)),
('%s' % self.iso_label, ' ')]
self.code = {}
self.code['show'] = {'sage': ''} # use default show names
self.code['class'] = {
'sage':
'E = EllipticCurve("%s1")\n' % (self.iso_label) +
'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)'
}