Re: Elliptic Curves over Number Fields

[William Stein]

On Sat, Mar 23, 2013 at 2:02 PM, burton newman <bnewm...@yahoo.com> wrote:
> Dear Dr. Stein,
>
> My name is Burton Newman and I am a graduate student at the University of
> Southern California, working with Sheldon Kamienny. I recently started
> playing with Sage and look forward to learning more about it.
>
> Right now I am interested in computing the integral points and evaluating
> the L-function of an elliptic curve over number fields (of small degree over
> Q). Despite much searching, it's not clear to me what Sage is currently
> capable of doing in this regard. Any guidance would be greatly appreciated!
>
> Thank you,
> Burton Newman
>
> P.S. I'd be happy to post this question in the appropriate forum if you
> prefer it.

The sage-nt mailing list is the right one. I've cc'd this email there.







--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[John Cremona]

On integral points on elliptic curves over number fields, code has
been written but is still residing in a patch on the trac server as
work is neeeded on it.

Burton, if you would like to contribute to getting this working well,
that would be appreciated!

On L-functions: Sage has Tim Dokchitser's ComputeL package but I think
there is no interface written to use that to work with L-functions of
elliptic curves over number fields other than Q. Someone may correct
me!

John

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[John Cremona]

You should ask Tim Dokchitser about the ComputeL algorithms. For
integral points on elliptic curves over number fields one source is
Smart & Stephens but the details need to be checked carefully. My
student Nook did this and wrote it as a Magma script, which some
people converted into Sage and that is what is at
http://trac.sagemath.org/sage_trac/ticket/10973.

John

On 25 March 2013 06:32, BN <bnewm...@gmail.com> wrote:
> Dear John,
>
> Thank you for the quick reply! I will read up on the problem of finding
> integral points and see what I can do. Is there any reference for the
> algorithm which you might recommend?
>
> Burton