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 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 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 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 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)'}