def make_isoclass_line(ec):
r""" for ec a curve object from the database, create a line of text to
match the corresponding raw input line from an isoclass file.
ec should be a dict with these fields:
'field_label', 'conductor_label', 'iso_label', 'number'
and optionally:
'isogeny_matrix'
Output line fields (15):
field_label conductor_label iso_label number isogeny_matrix
Sample output line:
2.0.4.1 65.18.1 a 1 [[1,6,3,18,9,2],[6,1,2,3,6,3],[3,2,1,6,3,6],[18,3,6,1,2,9],[9,6,3,2,1,18],[2,3,6,9,18,1]]
"""
mat = ''
if 'isogeny_matrix' in ec:
mat = str(ec['isogeny_matrix']).replace(' ', '')
else:
print("Making isogeny matrix for class %s" % ec['label'])
from lmfdb.ecnf.isog_class import permute_mat
from lmfdb.ecnf.WebEllipticCurve import FIELD
K = FIELD(ec['field_label'])
curves = nfcurves.find({
'field_label': ec['field_label'],
'conductor_label': ec['conductor_label'],
'iso_label': ec['iso_label']
}).sort('number')
Elist = [
EllipticCurve([K.parse_NFelt(x) for x in c['ainvs']])
for c in curves
]
cl = Elist[0].isogeny_class()
perm = dict([(i, cl.index(E)) for i, E in enumerate(Elist)])
mat = permute_mat(cl.matrix(), perm, True)
mat = str([list(ri) for ri in mat.rows()]).replace(" ", "")
output_fields = [
ec['field_label'], ec['conductor_label'], ec['iso_label'],
str(ec['number']), mat
]
return " ".join(output_fields)
def make_isoclass_line(ec):
r""" for ec a curve object from the database, create a line of text to
match the corresponding raw input line from an isoclass file.
ec should be a dict with these fields:
'field_label', 'conductor_label', 'iso_label', 'number'
and optionally:
'isogeny_matrix'
Output line fields (15):
field_label conductor_label iso_label number isogeny_matrix
Sample output line:
2.0.4.1 65.18.1 a 1 [[1,6,3,18,9,2],[6,1,2,3,6,3],[3,2,1,6,3,6],[18,3,6,1,2,9],[9,6,3,2,1,18],[2,3,6,9,18,1]]
"""
mat = ''
if 'isogeny_matrix' in ec:
mat = str(ec['isogeny_matrix']).replace(' ', '')
else:
print("Making isogeny matrix for class %s" % ec['label'])
from lmfdb.ecnf.isog_class import permute_mat
from lmfdb.ecnf.WebEllipticCurve import FIELD
K = FIELD(ec['field_label'])
curves = nfcurves.find({'field_label': ec['field_label'],
'conductor_label': ec['conductor_label'],
'iso_label': ec['iso_label']}).sort('number')
Elist = [EllipticCurve([K.parse_NFelt(x) for x in c['ainvs']]) for c in curves]
cl = Elist[0].isogeny_class()
perm = dict([(i, cl.index(E)) for i, E in enumerate(Elist)])
mat = permute_mat(cl.matrix(), perm, True)
mat = str([list(ri) for ri in mat.rows()]).replace(" ", "")
output_fields = [ec['field_label'],
ec['conductor_label'],
ec['iso_label'],
str(ec['number']),
mat]
return " ".join(output_fields)
