#32269 closed defect (fixed)

Isogenies prime degree fails on some CM curves

Reported by: Sachi Hashimoto Owned by:
Priority: major Milestone: sage-9.5
Component: elliptic curves Keywords: elliptic curves, isogeny, CM
Cc: Alex J. Best Merged in:
Authors: Alex J. Best Reviewers: Edgar Costa
Report Upstream: N/A Work issues:
Branch: 6b6dc19 (Commits, GitHub, GitLab) Commit: 6b6dc19fed27e3d0b5a4b529e1937986640aa14b
Dependencies: Stopgaps:

Status badges

Description

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]

Change History (13)

comment:1 Changed 15 months ago by Alex J. Best

Branch: u/alexjbest/isog-nf
Commit: 96561b332f35d1e9d56b190ce4a09221b779fb29
Status: newneeds_info
Work issues: wait for CI

New commits:

96561b3attempt to fix 32269

comment:2 Changed 15 months ago by Alex J. Best

Status: needs_infoneeds_review

comment:3 Changed 15 months ago by git

Commit: 96561b332f35d1e9d56b190ce4a09221b779fb29251c8297a5872756256a42e7a506c95ed5a91ed8

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

251c829output

comment:4 Changed 15 months ago by Alex J. Best

Authors: Alex J. Best

comment:5 Changed 15 months ago by Edgar Costa

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.

comment:6 Changed 14 months ago by Alex J. Best

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

comment:7 Changed 14 months ago by Edgar Costa

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

comment:8 Changed 14 months ago by git

Commit: 251c8297a5872756256a42e7a506c95ed5a91ed86b6dc19fed27e3d0b5a4b529e1937986640aa14b

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

6b6dc19fix doctest

comment:9 Changed 14 months ago by Alex J. Best

Work issues: wait for CI

comment:10 Changed 14 months ago by Edgar Costa

Status: needs_reviewpositive_review

comment:11 Changed 14 months ago by Edgar Costa

Reviewers: Edgar Costa

comment:12 Changed 14 months ago by Matthias Köppe

Milestone: sage-9.4sage-9.5

comment:13 Changed 13 months ago by Volker Braun

Branch: u/alexjbest/isog-nf6b6dc19fed27e3d0b5a4b529e1937986640aa14b
Resolution: fixed
Status: positive_reviewclosed
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