Re: ellperiods

[American Citizen <website.reader3@gmail.com>]

Bill

Thanks for that post. Appreciated.

- Randall

On 12/13/24 09:39, Bill Allombert wrote:
> On Fri, Dec 13, 2024 at 04:00:06PM +0000, John Cremona wrote:
> > It is not clear to me what ellperiods(e) returns when e is an ellinit for a
> > curve defined over a number field.
> ellperiods assume your curve is defined over R or C.
>
> > Also, if I want the period lattice for
> > all the embeddings of the fields into R or C, how would I do that?
> Just use E.omega.
>
> Otherwise, you would need to apply all the embeddings and then use ellperiods
> for each of them.
>
> > I am trying to see how many of the quantities appearing in the BSD
> > conjecture can be computed in GP, over a number field.
> Assuming the rank and generators are know, everything except the
> Tate-Shafarevich group, including the root number.
>
> > I am assuming
> > that we know generators somehow (ellgenerators() is not available), and
> > something to replace ellL1() so that we can get something like ellbsd().
> Just use lfun(E,1)
>
> > I may have missed functions which are already there for curves over number
> > fields -- if so, please tell me.
> May I suggest this tutorial ?
> https://pari.math.u-bordeaux.fr/Events/PARI2018b/talks/elliptic.pdf
> especially the last page.
>
> Cheers,
> Bill.