Re: ellintpoints(E) workaround

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

On Wed, Oct 07, 2026 at 02:21:43PM +0200, hermann@stamm-wilbrandt.de wrote:
> The curve's conductor is too high (if I determined it correctly):
> 
> ? E=ellinit([-14776, -670031]);
> ? ellglobalred(E)[1]
> 447294352204

Correct.

> Because I searched for integral points I would not have looked at
> ellratpoints.
> Doc says to look for hyperellratpoints for description of h.
> Seeing
> "- a vector [N, D] with D ≤ N : find the points [n/d, y] with |n| ≤ N , d ≤
> D."
> I know understand that 2nd vector entry 1 means only integral points.

Yes D is the bound on the denominator.

> But sagemath E.integral_points() is called without height.
> It seems to use Baker bounds, not sure.
> But how to choose H for ellratpoints(E,[H,1])?

This is the problem... this is difficult because first the resulut need to
be proven and secondly it must not be too large to be usable.
That is why I did not implement it in PARI.

> I needed to determine the generators, but ellgenerators(E) failed.

ellgenerators is only for curves in Cremona database.
You can use ellrank:

? ellrank(E)
%3 = [4,4,0,[[-80,7],[-73,140],[-66,133],[-60,23]]]

Cheers,
Bill