Re: Bug in elltors

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

On Mon, 12 Aug 2002, Karim BELABAS wrote:
> 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.
> > [...]
[...]
> 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 ?

Update: John Cremona has been so kind as to send me his test suite ( 5114
curves, including several examples for all possible torsion groups ).

The current CVS code passes successfully [ gp refuses to answer thrice due to
insufficient precision, but gives the correct result in these 3 cases also,
once precision is increased ].

Unfortunately, so does the old (incorrect) code, which fails on the
aforementioned two curves !

    Karim.
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Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
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