fix random doctest failure in EllipticCurveHom_velusqrt

[yyyyx4]

As reported in #34303 comment:25, EllipticCurveHom_velusqrt accidentally computes an irrational isogeny for curves defined over GF(3) with 7 rational points. The reason is that the computation internally requires a point lying outside the kernel, which only in this one specific case will be defined over a cubic instead of a quadratic extension. This in turn implies the linear factors in the numerator of the isogeny won't match up in conjugate pairs, causing the problem.

Quick fix: Simply restrict the implementation to degrees ≥ 9. Since the older EllipticCurveIsogeny implementation is much faster for degrees this small anyway, this restriction won't be a problem for any remotely realistic code.

CC: @antonio-rojas

Component: elliptic curves

Author: Lorenz Panny

Branch/Commit: 467eda5

Reviewer: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/34467

[kwankyu]

comment:2

How about adding a doctest for this problematic case with an explanation and a link to this ticket?

[sagetrac-git]

Changed commit from 0872312 to 467eda5

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

c71dc3f	increase minimum degree for Îlu formulas to 9
467eda5	add failing example

[yyyyx4]

comment:4

Done.

[kwankyu]

comment:5

Thanks. LGTM.

[kwankyu]

Reviewer: Kwankyu Lee

[vbraun]

Changed branch from public/increase_velusqrt_minimum_degree_to_9 to 467eda5