Elliptic curves with large Tate-Shafarevich groups over ${\mathbb{F}}_q(t)$

Richard Griffon, Guus de Wit

Let ${\mathbb{F}}_q$ be a finite field of odd characteristic $p$. We exhibit elliptic curves over the rational function field $K={\mathbb{F}}_q(t)$ whose Tate-Shafarevich groups are…