American Citizen on Wed, 04 Feb 2026 00:28:44 +0100


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what's going on here?


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