Use Pari/gp for learning Elliptic Curves and ECPP

[tony.reix@laposte.net]

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 ?

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 ?

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.

I've already found that Denomme-Savin/Tsumura method for proving the primality of Fermat numbers SEEMS (as a candidate PRP test) to work for Wagstaff numbers. However, the method of their proof CANNOT be used for Wagstaff numbers, which are not smooth.

So, I'd like to find a Pari/gp code implementing ECPP. Efficiency is not the goal. Learning is the goal.

Thx

Tony