Re: ellisisom?

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

On Fri, May 03, 2024 at 12:34:21PM +0000, Ahmad Mostafa Ismail El-Guindy wrote:
> Hello,
> 
> In this link
> https://pari.math.u-bordeaux.fr/dochtml/html/Elliptic_curves.html
> 
> there is the description below of the function ellisisom
> 
> ellisisom(E, F)
> Return 0 if the elliptic curves E and F defined over the same number field are not isomorphic, otherwise return [u,r,s,t] suitable for ellchangecurve, mapping E to F.
> 
> The library syntax is GEN ellisisom(GEN E, GEN F).
> 
> However, this function is not present either in the current version ( GP/PARI CALCULATOR Version 2.15.5 (released)) or in its documentation (naturally)
> 
> https://pari.math.u-bordeaux.fr/dochtml/html-stable/
> 
> My question is whether there is a substitute (and was there a reason for the removal)?

It was not removed, ellisisom is currently only available in the development version.

Below is a GP implementation if you need it:

myellisisom(E,F)=
{
  my(u,r,s,t);
  if (E.j!=F.j, return(0));
  if (E.j==0,
       if(!ispower(E.c6/F.c6,6,&u),return(0))
     ,E.j==1728,
       if(!ispower(E.c4/F.c4,4,&u),return(0))
     , if(!ispower(F.c4*E.c6/(F.c6*E.c4),2,&u),return(0)));
  s = (u*F.a1-E.a1)/2;
  r = (u^2*F.a2 + s*E.a1 - E.a2 + s^2)/3;
  t = (u^3*F.a3 - r*E.a1 - E.a3)/2;
  [u,r,s,t];
}

Cheers,
Bill