PS. Sorry, copy-paste error, I missed out the first line of the example, which was the usual incantation "sage: R.<x> = PolynomialRing(QQ)".
On Thu, 25 Nov 2021 at 13:26, David Loeffler <[email protected]> wrote: > If I have two elliptic curves over a number field, then Sage seems to know > how to test if they are isogenous, and find the minimal degree of an > isogeny between them; but is there any way of computing the actual isogeny? > > Here's an example (the Q-curve 45.1-a1 over Q(sqrt(5)) and its Galois > conjugate): > > sage: K.<a> = NumberField(R([-1, -1, 1])) > sage: E = > EllipticCurve([K([0,1]),K([1,1]),K([1,0]),K([-7739,-4364]),K([-296465,-255406])]) > sage: si = K.Hom(K).list()[-1] > sage: E2 = E.base_extend(si) > sage: E.is_isogenous(E2) > True > sage: E.isogeny_degree(E2) > 4 > > There is a method "E.isogeny(...)" but it wants an explicit kernel. The > docstring says that the kernel will be computed automatically if I specify > "kernel=None", but that seems to result in an error: > > sage: E.isogeny(kernel=None, codomain=E2, degree=4) > [...] > ValueError: The two curves are not linked by a cyclic normalized isogeny > of degree 4 > > I'm not sure what "normalized" means here, but there is definitely a > cyclic degree 4 isogeny from E to E2. What do I need to do to persuade Sage > to find it? > > Regards, David > > -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/8ebce2b8-316c-4765-8236-e729f7b67b8dn%40googlegroups.com > <https://groups.google.com/d/msgid/sage-nt/8ebce2b8-316c-4765-8236-e729f7b67b8dn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-nt" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-nt/CANDN%3Dhyd3TeUXPx5VamBkKSDA96epFfc41Yjphptb9pRwWMfZw%40mail.gmail.com.
