Opened 8 years ago

Closed 8 years ago

# simon_two_descent sometimes gives wrong answers

Reported by: Owned by: pbruin critical sage-6.2 elliptic curves simon_two_descent cremona, mmasdeu Peter Bruin Marc Masdeu Reported upstream. No feedback yet. 275e4be 275e4bef0c5027517163a50248cf417308d6bde7

### Description

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`.)

### comment:1 Changed 8 years ago by pbruin

• Branch set to u/pbruin/16022-simon_two_descent_bug
• Commit set to 275e4bef0c5027517163a50248cf417308d6bde7
• Status changed from new to needs_review

### comment:2 Changed 8 years ago by pbruin

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)
```

### comment:3 Changed 8 years ago by mmasdeu

• Reviewers set to Marc Masdeu
• Status changed from needs_review to positive_review

### comment:4 follow-up: ↓ 5 Changed 8 years ago by wuthrich

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.

### comment:5 in reply to: ↑ 4 Changed 8 years ago by pbruin

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.)

### comment:6 Changed 8 years ago by vbraun

• Branch changed from u/pbruin/16022-simon_two_descent_bug to 275e4bef0c5027517163a50248cf417308d6bde7
• Resolution set to fixed
• Status changed from positive_review to closed
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