def genus1_lookup_equation_nf(rec):
assert rec['g'] == 1
# make base field
nf_matches = list(db.nf_fields.search({'coeffs': rec['base_field']}))
if len(nf_matches) == 0:
return None
else:
nf_rec = nf_matches[0]
# make curve
f, h = curve_string_parser(rec)
ainvs = hyperelliptic_polys_to_ainvs(f, h)
E = EllipticCurve(ainvs)
K = E.base_field()
j = E.j_invariant()
j_str = NFelt(j)
j_matches = list(
db.ec_nfcurves.search({
"field_label": nf_rec['label'],
"jinv": j_str
}))
for r in j_matches:
ainvs2 = parse_ainvs(K, r['ainvs'])
E2 = EllipticCurve(ainvs2)
assert E.base_field() == E2.base_field()
if E.is_isomorphic(E2):
return r['label']
#print("Curve not found in database")
return None
def genus1_lookup_equation_QQ(rec):
assert rec['g'] == 1
f, h = curve_string_parser(rec)
ainvs = hyperelliptic_polys_to_ainvs(f, h)
E = EllipticCurve(ainvs)
j = E.j_invariant()
for r in db.ec_curves.search({"jinv": str(j)}):
ainvs2 = r['ainvs']
E2 = EllipticCurve(ainvs2)
if E.is_isomorphic(E2):
return r['lmfdb_label']
#print("Curve not found in database")
return None
def genus2_lookup_equation(rec):
f, h = curve_string_parser(rec)
return genus2_lookup_equation_polys(str([f, h]))