simon_two_descent sometimes gives wrong answers

[pjbruin]

The current version of Denis Simon's 2-descent program (in Sage since #11005) has a bug:

sage: K.<y> = NumberField(x^4 + x^2 - 7);
sage: E = EllipticCurve(K, [1, 0, 5*y^2 + 16, 0, 0])
sage: E.simon_two_descent(lim1=2, limtriv=3)
[0, 0, []]

The rank is in fact 1, and a correct return value would be (1, 1, [(-369/25*y^3 + 539/25*y^2 - 1178/25*y + 1718/25 : -27193/125*y^3 + 39683/125*y^2 - 86816/125*y + 126696/125 : 1)]).

This ticket is just to fix this as quickly as possible; it should eventually be fixed in a new version of Simon's program.

(See #15608 for a list of tickets related to simon_two_descent.)

Upstream: Reported upstream. No feedback yet.

CC: @JohnCremona @mmasdeu

Component: elliptic curves

Keywords: simon_two_descent

Author: Peter Bruin

Branch/Commit: 275e4be

Reviewer: Marc Masdeu

Issue created by migration from https://trac.sagemath.org/ticket/16022

[pjbruin]

Branch: u/pbruin/16022-simon_two_descent_bug

[pjbruin]

Commit: 275e4be

[pjbruin]

comment:2

To reproduce this directly in GP:

\r ell.gp
K = bnfinit(y^4 + y^2 - 7);
a = Mod(y, K.pol);
E = [1, 0, 5*a^2 + 16, 0, 0];
DEBUGLEVEL_ell = 2;
LIM1 = 2;
LIMTRIV = 3;
bnfellrank(K, E)

[mmasdeu]

Reviewer: Marc Masdeu

[chriswuthrich]

comment:4

Comment moved from #10745:

I see that you changed ell.gp. Is this good ? It is very very likely that the next update of simon's scripts will forget to make this patch-fix of a upstream file. Would it not be better to tell the author to change this in his version and we update our file ? This is a genuine question as I am not sure what is better. One thing to bear in mind is that it seems that Denis has not been very active on the bugs in his script recently.

[pjbruin]

comment:5

Replying to @categorie:

I see that you changed ell.gp. Is this good ? It is very very likely that the next update of simon's scripts will forget to make this patch-fix of a upstream file. Would it not be better to tell the author to change this in his version and we update our file ? This is a genuine question as I am not sure what is better. One thing to bear in mind is that it seems that Denis has not been very active on the bugs in his script recently.

I reported the bug to Denis and sent him the same patch used for this ticket. Something similar happened with #15483. So far, these are the only two tickets in which changes to ell.gp were made. Hopefully he will make these fixes (or alternative ones) in the next version. (We don't know when that will be, but the last version of ell.gp dates from 2011, while all his other programs were updated last January.)

[vbraun]

Changed branch from u/pbruin/16022-simon_two_descent_bug to 275e4be