Re: Support for elliptic curves over number fields

[John Cremona <john.cremona@gmail.com>]

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?

John

>
> Cheers,
> Bill
>