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 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'])]
