Re: what's going on here?

[Aurel Page <aurel.page@normalesup.org>]

Dear Randall,

You simply need to increase the search effort a bit:

? ellrank(E,1)
% = [1, 1, 2, [[1/4, 1/8]]]

Maybe we can tune the default better, I am not sure.

Best,
Aurel

On 04/02/2026 00:28, American Citizen wrote:
> This is a question on the ellrank() command.
>
> I have e = [0, -3860/957, 0, 965/957, 0]
>
> ? E=ellinit(e);
> ? ellrank(E)
> %7 = [1, 1, 2, []]
>
> Huh??? what?
>
> ? [x,y]=[1/4,-1/8]
> %8 = [1/4, -1/8]
> ? ellordinate(E,1/4)
> %9 = [1/8, -1/8]
>
> this is a rather simple elliptic curve of rank=1,
>
> mwrank confirms the Mordell-Weil basis of [1/4,-1/8]
>
> I am using
>
> >            GP/PARI CALCULATOR Version 2.18.1 (development 
> > git-5d3c5ac62a)
> >             amd64 running linux (x86-64/GMP-6.3.0 kernel) 64-bit version
> >                compiled: Aug 23 2025, gcc version 13.3.0 (SUSE Linux)
> >                       threading engine: pthread, nbthreads = 6
> >                    (readline v7.0 enabled, extended help enabled)
> if I use ellrank(E,1) then I get the MW basis.
>
> I am just curious as to why this is missed, with no search effort 
> specified. Should the ellrank command be rewritten with search effort 
> set to 1 automatically?
>
> Randall