class EC(object):
def __init__(self, A, C=None):
"""
Cy² = Cx³ + Ax + Cx
"""
# Internally, we represent it as a Sage elliptic curve.
a = A / C if C is not None else A
self.ec = EllipticCurve([0, a._sage(), 0, 1, 0])
def j(self):
j = self.ec.j_invariant()
return GF(j.parent().characteristic(), *j.polynomial().list())
def point(self, x):
return Point(self, x)
def four_isogeny(self, gen):
pass
def three_isogeny(self, gen):
pass
def secret_isogeny(self, gen):
pass
def __repr__(self):
return repr(self.ec)
def _sage(self):
return self.ec
def test_semi_stable_frobenius_polynomial_t():
# an example where the frobenius polynomial depends on the purely ramified extension
# we make
x = polygen(QQ)
K = QQ.extension(x - 1, "one")
E = EllipticCurve(K, [49, 343])
assert E.discriminant() == -(2**4) * 31 * 7**6
assert E.j_invariant() == K(2**8 * 3**3) / 31
f1 = semi_stable_frobenius_polynomial(E, K * 7, 1)
f2 = semi_stable_frobenius_polynomial(E, K * 7, -1)(x=-x)
assert f1 == f2
