Re: ellheegner

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On 23 June 2014 20:07, Ariel Martin Pacetti <apacetti@dm.uba.ar> wrote:
> Dear users,
>
> is there a way to compute a rational heegner point chosing the discriminant?
> This should be implemented in the ellheegner routine, but such choice is not
> available (is there a reason for that?). I remember this was done in an old
> package from Peter Green.

Hello Ariel,
Could you provide an example ?

This can be done with minimal change to the PARI source code.

Hwoever, PARI definition of the Heegner point is 
"A  non-torsion  rational  point  on  the curve,  whose canonical height is equal to the
product of the elliptic regulator by the analytic Sha"

which means the choice of discriminant has a very small effect on the result.
In practice, PARI chose the discriminant so that the series is as fast as
possible to compute.

Cheers,
Bill.