Re: general educational question on elliptic curve isogenies and moving points around

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

Bill

What I am expecting as a function operator is something like

map_iso(F,E,pt) = [operate_on_x, operate_on_y] where x=p[1] and y=p[2] 
using the f,g,h polynomials from the ellisomat results. derived from the 
minimal model maps of the elliptic curves F and E.

I would like to see the operator function f given like a GP-Pari 
function say q = f(F,E,p) which outputs point q on F.

The way I worked this was take E (given elliptic curve), find M (minimal 
model of E), move points to M, then find N (minimal model of F) and 
carefully compare the ellisomat results for both elliptic curves M and 
N, to find a match on the E(a4,a6) curves. Once this is found,  I move 
points on E to M, then move points from M to N, then move the points 
from N to F. As you all know, this has to be carefully done.

Using the curves I have, which have 8 torsion points, I found that 
usually 4 isogeny types of lifts are possible (matching E(a4,a6) curves, 
but I just chose the first possible isogeny lift (where the E(a4,a6) 
curves match)

I hope this is clear.

Anyone is welcome to comment.

On 11/25/23 15:06, Bill Allombert wrote:
> On Sat, Nov 25, 2023 at 02:42:42PM -0800, American Citizen wrote:
> > I was able to write a script which successfully found the isogeny and dual
> > isogeny on the mimimal models of isomorphisms and mapped the point back
> > successfully through the forward and reverse mapping.
> >
> > I guess my only question is how to us the apply command to specifically
> > apply  x.y value from a known point to the isogeny or its dual then creating
> > the point [f/h^2, g/h^3] from that apply possibly all on one line.
> Use ellisogenyapply ?
>
> Cheers,
> Bill.