#7096: bug in dual isogeny computation
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-4.2
Component: elliptic curves | Keywords: elliptic curve isogeny
Work_issues: | Author:
Reviewer: | Merged:
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Comment(by wuthrich):
I found another issue with isogenies.
{{{
E = EllipticCurve('11a1')
E2 = EllipticCurve('11a2')
E2.isogeny(None,codomain=E1,degree=5)
}}}
fails with
{{{
ValueError: Codomain parameter must be isomorphic to computed codomain
isogeny
}}}
while {{{E.isogeny(None,codomain=E2,degree=5)}}} works fine. The reason is
that the algorithm for computing the kernel polynomial in
{{{compute_isogeny_starks}}} is only valid for '''normalised''' isogenies.
Stark's algorithm is implemented in ell_curve_isogeny.py from scratch and
so it contains the computation of the formal expansion of the Weierstrass
p function. I wonder if we should add as another possible algorithm to do
the same sort of computation, but using the already existing code for
formal groups instead. ....
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7096#comment:7>
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