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

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

On Mon, 27 Nov 2023 at 14:03, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> wrote:

On Sun, Nov 26, 2023 at 05:32:03PM -0800, American Citizen wrote:
> Using
>
> All results = 0 for using K[1] and trying the other 7 curves.
>
> for example ellisisom(K[1],K[2]) = 0
>
> What am I doing wrong?

Your curves are isogenous but not isomorphic.

I suppose you want to do:

E=ellinit(K[1]);
S=ellisomat(E)[1];
vector(#K,i,apply(e->ellisisom(ellinit(e[1]),ellinit(K[i])),S))
%4 = [[[1,1/12,1/2,0],0,0,0,0,0,0,0],[0,[2,1/3,1,0],0,0,0,0,0,0],[0,0,[2,1/3,1,0],0,0,0,0,0],[0,0,0,[4,4/3,2,0],0,0,0,0],[0,0,0,0,[1,1/12,1/2,0],0,0,0],[0,0,0,0,0,[1,1/12,1/2,0],0,0],[0,0,0,0,0,0,[1,1/12,1/2,0],0],[0,0,0,0,0,0,0,[1,1/12,1/2,0]]]

So you get the correspondance between ellisomat output and your list, with the variable change.

Cheers,
Bill.

PS: I join a new version of ellisisom which fix a typo if j=0 or 1728.

That function will need to be more complicated for use in characteristics 2 or 3!  If you want to see the details, I implemented it in Sage a long time ago -- see https://github.com/sagemath/sage/blob/develop/src/sage/schemes/elliptic_curves/weierstrass_morphism.py, lines 223-372, where the last 10 lines or so (which cover characteristics not 2,3) are similar to Bill's gp function.

[I hope I have not offended any rules of etiquette by citing Sage here!]

John