Re: New experimental GP interface for elliptic curves over finite fields

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, Jul 12, 2012 at 07:47:37PM +0200, Bill Allombert wrote:
> On Thu, Jun 07, 2012 at 12:16:11PM +0200, Bill Allombert wrote:
> > Dear PARI developers,
> > 
> > I have added a new experimental interface for elliptic curves over finite
> > fields.
> > A new function ellffinit is provided to create curves over finite fields:
> > 
> > Create a curves over F_7:
> > ? E=ellffinit([1,3],7);
> > 
> > Create a curves over F_101^3:
> > ? a=ffgen(ffinit(101,3),'a);
> > ? E=ellffinit([1,a^3],a);
> > 
> > (for technical reasons, the characteristic must be >3. This will be fixed eventually.)
> 
> I have just added support for ordinary curves over finite field of characteristic 2.
> 
> Also I have added a flag to ellffinit to disable the factorisation of d1. This allows
> to test the computation of the number of point of curves over large fields.

I have added support for flag=2 to ellffinit, which assume that the underlying group
is cyclic. Note that if the group is not cyclic, ellcard will still return the correct
result. This saves time when we are not interested in the group structure.

Anyway, ellffinit should be integrated in ellinit in the future.

Cheers,
Bill.