def isogeny_codomain(self, kernel, degree=None):
r"""
Returns the codomain of the isogeny from self with given
kernel.
INPUT:
- ``kernel`` - Either a list of points in the kernel of the isogeny,
or a kernel polynomial (specified as a either a
univariate polynomial or a coefficient list.)
- ``degree`` - an integer, (default:None) optionally specified degree
of the kernel.
OUTPUT:
An elliptic curve, the codomain of the separable normalized
isogeny from this kernel
EXAMPLES::
sage: E = EllipticCurve('17a1')
sage: R.<x> = QQ[]
sage: E2 = E.isogeny_codomain(x - 11/4); E2
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 1461/16*x - 19681/64 over Rational Field
"""
return isogeny_codomain_from_kernel(self, kernel, degree=None)
def isogeny_codomain(self, kernel, degree=None):
r"""
Returns the codomain of the isogeny from self with given
kernel.
INPUT:
- ``kernel`` - Either a list of points in the kernel of the isogeny,
or a kernel polynomial (specified as a either a
univariate polynomial or a coefficient list.)
- ``degree`` - an integer, (default:None) optionally specified degree
of the kernel.
OUTPUT:
An elliptic curve, the codomain of the separable normalized
isogeny from this kernel
EXAMPLES::
sage: E = EllipticCurve('17a1')
sage: R.<x> = QQ[]
sage: E2 = E.isogeny_codomain(x - 11/4); E2
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - 1461/16*x - 19681/64 over Rational Field
"""
return isogeny_codomain_from_kernel(self, kernel, degree=None)