Ordinary elliptic curves of high rank over ${\bar{F}}_p(x)$ with constant j-invariant

Irene I. Bouw, Claus Diem, Jasper Scholten

We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over ${\bar{F}}_p(x)$ with arbitrary high rank and consta…