Isogenies prime degree fails on some CM curves

[sachihashimoto]

The code:

K.<a> = QuadraticField(-11)
E = EllipticCurve(K, [0,1,0,-117,-541])
E.isogenies_prime_degree(53)

returns an empty list. But, since E has CM by the ring of integers of K, it has to have an isogeny of degree p for p splitting in K, so this doesn't make sense.

If you import isogenies_prime_degree_general from isogeny_small_degree.py then

isogenies_prime_degree_general(E,53) 

correctly returns

[Isogeny of degree 53 from Elliptic Curve defined by y^2 = x^3 + x^2 + (-117)*x + (-541) over Number Field in a with defining polynomial x^2 + 11 with a = 3.316624790355400?*I to Elliptic Curve defined by y^2 = x^3 + x^2 + (98560*a+42123)*x + (-12561472*a-61946205) over Number Field in a with defining polynomial x^2 + 11 with a = 3.316624790355400?*I,
 Isogeny of degree 53 from Elliptic Curve defined by y^2 = x^3 + x^2 + (-117)*x + (-541) over Number Field in a with defining polynomial x^2 + 11 with a = 3.316624790355400?*I to Elliptic Curve defined by y^2 = x^3 + x^2 + (-98560*a+42123)*x + (12561472*a-61946205) over Number Field in a with defining polynomial x^2 + 11 with a = 3.316624790355400?*I]

CC: @alexjbest

Component: elliptic curves

Keywords: isogeny, CM

Author: Alex J. Best

Branch/Commit: 6b6dc19

Reviewer: Edgar Costa

Issue created by migration from https://trac.sagemath.org/ticket/32269

[alexjbest]

Branch: u/alexjbest/isog-nf

[alexjbest]

Commit: 96561b3

[alexjbest]

New commits:

96561b3

attempt to fix 32269

[alexjbest]

Work Issues: wait for CI

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

251c829

output

[sagetrac-git]

Changed commit from 96561b3 to 251c829

[alexjbest]

Author: Alex J. Best

[edgarcosta]

comment:5

LGTM, but that test with ell = 53 is not going to fly.

Why not ell = 37? it is equally broken and takes 1/6 of the time.

[alexjbest]

comment:6

@edgarcosta, right the example in code uses l=37, it might still need marking as # long time though, I'm not sure.

[edgarcosta]

comment:7

Upsidaisy! Ignore my comment then.

I was hoping that the patch bot would tell us what to do regarding the necessity of the marking as # long

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

6b6dc19

fix doctest

[sagetrac-git]

Changed commit from 251c829 to 6b6dc19

[alexjbest]

Changed work issues from wait for CI to none

[edgarcosta]

Reviewer: Edgar Costa

[vbraun]

Changed branch from u/alexjbest/isog-nf to 6b6dc19