Re: a hopeful request

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

Randall, the formulas for this are in my book. I'm sure Bill must have implemented them in libpari, but they are possibly not yet exposed as GP functions.

John

On Sat, 2 Mar 2024, 01:12 American Citizen, <website.reader3@gmail.com> wrote:

To all:

I have been looking for this for a long time.

Suppose I have an elliptic curve in Weierstrass format [a1,a2,a3,a4,a6]
and a two-covering or quartic a*x^4 + b*x^3 + c*x^2 + d*x + e and they
share the same invariants, the I invariant and the J invariant.

Is it possible to develop the forward and inverse maps for points on
either the elliptic curve mapping to the quartic two-cover, or the
points on the two-cover mapping back to the elliptic curve?

I would like to obtain the forward and inverse maps for points on either
the elliptic curve -> quartic or quartic -> elliptic curve

Thank you for letting me know if this is possible and how to set this up
in GP-Pari

Randall