2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67366We 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 constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/ell Z)^*/<-1> (ell an odd prime) there exists a hyperelliptic curve over $\bar F_p$ whose Jacobian is isogenous to a power of one ordinary elliptic curve.15 pages, 0 figures, LaTeXNumber TheoryAlgebraic Geometry11G05 (Primary); 11G20; 14H40; 14H52 (Secondary)text