Re: Support for elliptic curves over number fields

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

On Sat, Jul 16, 2016 at 05:44:07PM +0100, John Cremona wrote:
> On 16 July 2016 at 17:06, Bill Allombert
> <Bill.Allombert@math.u-bordeaux1.fr> wrote:
> > Dear PARI developers,
> >
> > We have added basic support for elliptic curves over number fields and L
> > function of elliptic curves over number fields.
> 
> Excellent!  Some of this functionality is already mentioned on web
> pages such as http://www.lmfdb.org/EllipticCurve/3.3.148.1/356.1/a/1
> (after clicking the "Show commands for ... Pari/gp" near the top.  If
> those commands are not correct, please let me know (they were written
> by Aurel).  I notice that he did not include the field as a parameter
> in the ellinit().
> 
> >
> > This is an example:
> >
> > ? N=nfinit(a^3-26);
> > ? E=ellinit([a,0,1,0,0],N);
> > ? lfun(E,1)
> > %4 = 0.24961216776576924744553489082015201012
> 
> Are there plans to include Denis Simon's gp scripts for 2-descent,
> over Q and over number fields, as standard?

Yes, but this requires changes to the way S-units of number fields are
computed.

Cheers,
Bill.