Re: Use Pari/gp for learning Elliptic Curves and ECPP

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

On Thu, Jul 13, 2023 at 11:03:35PM +0200, tony.reix@laposte.net wrote:
> Hi,
> 
> I'd like to learn Elliptic Curves and ECPP by using Pari/gp.
> I'm now reading L. C. Washington's book.
> 
> I've already found:
>    http://pari.math.u-bordeaux.fr/Events/PARI2018b/talks/elliptic.pdf‌;
>    http://pari.math.u-bordeaux.fr/dochtml/html/Elliptic_curves.html
>    http://pari.math.u-bordeaux.fr/Events/PARI2017c/talks/ecc_en.pdf‌‌;
>    http://pari.math.u-bordeaux.fr/Events/PARIday2021/talks/ellrank.pdf‌‌;
>    http://pari.math.u-bordeaux.fr/Events/PARI2018/talks/ecpp.pdf‌;
> that I'll have to read and experiment with.
> Are there more Pari/gp documents I should use ?

This one:
https://pari.math.u-bordeaux.fr/Events/PARI2015/talks/hamish.pdf

> About the last paper (by Jared Asuncion), it talks about a  "ecpp()" function, which is not provided by Pari/gp AFAIK.
> Is there some Pari/gp code implementing ECPP somewhere ?

Yes, isprime and primecert.

> My goal is to understand and experiment ECPP with Pari/gp with a special kind
> of numbers (Wagstaff numbers) and see if I can find "constants" for different
> instances of this kind of numbers.

Well, it happens I proved the primality of (2^95369 + 1)/3 using ECPP.
The certificates are there:

https://pari.math.u-bordeaux.fr/pub/bill/primecerts/primo-W95369.out.gz
https://pari.math.u-bordeaux.fr/pub/bill/primecerts/cert-W95369.gz

Cheers,
Bill.