Re: ellintpoints(E) workaround

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

On Wed, Oct 07, 2026 at 12:52:18AM +0200, hermann@stamm-wilbrandt.de wrote:
> An elliptic curve can have only a finite number of points with integer
> coordinates by Siegel's theorem.
> 
> PARI/GP seems not to have a function to determine the integral points of
> elliptic curve E.
> 
> My workaround ellintpoints(E) (named after existing ellratpoints(E)) calls
> out to sagemath E.integral_points():
> 
> sage(cmd) = eval(externstr(Str("sage -q -c \"", cmd, "\""))[1]);
> 
> ellintpoints(E) = {
>   sage(Str("print([[int(P[0]), int(P[1])] for P in EllipticCurve(",
>        E[1..5],").integral_points()])"));
> }

What gives your function for
E = [1, -1, 1, -11, 16]
and
E = [0, 1, 0, 44, -847]

Cheers,
Bill.