def EllipticCurve_to_ecnf_dict(E):
"""
Make the dict that should be fed to `make_curves_line` in `lmfdb/scripts/ecnf/import_utils.py`.
It sets `iso_label`, 'a' and `number` to '1' and `cm` and `base_change` to '?'
INPUT:
* E - A sage elliptic curve over a number field
"""
E = EllipticCurve_polredabs(E)
K = E.base_field()
WNF = WebNumberField.from_polredabs(K.polynomial())
ainvs = [map(str,ai) for ai in map(list,E.a_invariants())]
conductor = E.conductor()
conductor_str = "".join(str([conductor.norm()]+list(conductor.gens_two())).split())
ec = {'field_label':WNF.label,
'conductor_label':ideal_label(conductor),
'iso_label':'a',
'number':'1',
'conductor_ideal':conductor_str,
'conductor_norm':str(conductor.norm()),
'ainvs':ainvs,
'cm':'?',
'base_change':'?'}
return ec
def EllipticCurve_to_ecnf_dict(E):
"""
Make the dict that should be fed to `make_curves_line` in `lmfdb/scripts/ecnf/import_utils.py`.
It sets `iso_label`, 'a' and `number` to '1' and `cm` and `base_change` to '?'
INPUT:
* E - A sage elliptic curve over a number field
"""
E = EllipticCurve_polredabs(E)
K = E.base_field()
WNF = WebNumberField.from_polredabs(K.polynomial())
ainvs = [map(str, ai) for ai in map(list, E.a_invariants())]
conductor = E.conductor()
conductor_str = "".join(
str([conductor.norm()] + list(conductor.gens_two())).split())
ec = {
'field_label': WNF.label,
'conductor_label': ideal_label(conductor),
'iso_label': 'a',
'number': '1',
'conductor_ideal': conductor_str,
'conductor_norm': str(conductor.norm()),
'ainvs': ainvs,
'cm': '?',
'base_change': '?'
}
return ec
def G_name(self):
"""
More-or-less standardized name of the abstract group
"""
import re
wnf = WebNumberField.from_polredabs(self.polredabs())
if not wnf.is_null():
mygalstring = wnf.galois_string()
if re.search('Trivial', mygalstring) is not None:
return '$C_1$'
# Have to remove dollar signs
return mygalstring
if self.polredabs().degree() < 12:
# Let pari compute it for us now
from sage.all import pari
galt = int(list(pari('polgalois(' + str(self.polredabs()) + ')'))[2])
from lmfdb.transitive_group import WebGaloisGroup
tg = WebGaloisGroup.from_nt(self.polredabs().degree(), galt)
return tg.display_short()
return self._data["G-Name"]
def G_name(self):
"""
More-or-less standardized name of the abstract group
"""
import re
wnf = WebNumberField.from_polredabs(self.polredabs())
if not wnf.is_null():
mygalstring = wnf.galois_string()
if re.search('Trivial', mygalstring) is not None:
return '$C_1$'
# Have to remove dollar signs
return mygalstring
if self.polredabs().degree() < 12:
# Let pari compute it for us now
from sage.all import pari
galt = int(list(pari('polgalois(' + str(self.polredabs()) + ')'))[2])
from lmfdb.transitive_group import WebGaloisGroup
tg = WebGaloisGroup.from_nt(self.polredabs().degree(), galt)
return tg.display_short()
return self._data["G-Name"]
def wnf(self):
return WebNumberField.from_polredabs(self.polredabs())
def wnf(self):
return WebNumberField.from_polredabs(self.polredabs())
