2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223506We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter $d \to\infty$. This is perhaps unexpected since by a result of A. Brumer, the average rank for all elliptic curves over a function field of positive characteristic is asymptotically bounded above by 2.3.Number TheoryAlgebraic Geometry11N25, 11R37, 14H52text