Re: New GP function ellrank (2-descent)

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

On Wed, Feb 17, 2021 at 05:05:44PM +0000, John Cremona wrote:
> equivalence class, some quartics have smaller rational points than
> others!  I cannot see how that helps, really -- it will depend on how
> you are constructing the different quartics.  If it is random (which I
> do not expect) then it is not so different from trying random rational
> x and hoping it gives a point.  Not exactly -- it is more like, take a
> random transform and then look for rational points corresponding to
> transforms near that one.

Using S-units, we have a rather efficient process to find small representatives
of a given Selmer class. However such representatives are not unique, and
by multiplying by a random small square we can easily find others.
There is no reason to assume the first one we find is "better" than the
others.

Cheers,
Bill