Re: Bug in elltors

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Fri, 19 Jul 2002, Mark J Watkins wrote:
[directly to me. Forwarded to pari-dev]

> Every version of PARI which I have computes the torsion group for
> [0,0,0,-1032,-1031] and [0,0,0,-6648,208633] incorrectly,
> saying they have C2 torsion instead of C6 torsion.
>
> In the function torselldoud (in one of the cases where b%4!=0)
>
>     case 2: /* 1 point of order 2: w2 / 2 or (w1+w2) / 2 */
>       for (i=5; i>1; i-=2)
>       {
>         if (b%i!=0) continue;
>         w1j = gdivgs(w1,i);
> /*!!*/  p = torspnt(e,pointell(e,gadd(w22,w1j),prec),i+i);
>         if (p) { k = 2*i; break; }
>       }
>       if (!p) { p = tor2; k = 2; }
>       tor2 = NULL; break;
>
> Here it turns out that one needs to check gadd(w1j,gadd(w22,w12)) also.
> I don't know if a similar test needs to be added elsewhere in this.

This is a typo. It should have been gadd(w1j, w), where w is the 2-torsion
point we already about [ often w2/2, but here it was (w1+w2)/2 ].

Fixed in CVS [and code somewhat cleaned].

I've rechecked the code and could find no other obvious slip. Does anybody
have an extensive database of curves together with their torsion group that
we could use to thoroughly check the routine ?

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
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