On the arithmetic of a family of twisted constant elliptic curves

Richard Griffon, Douglas Ulmer

Let ${\mathbb{F}}_r$ be a finite field of characteristic $p>3$. For any power $q$ of $p$, consider the elliptic curve $E=E_{q,r}$ defined by $y^2=x^3+t^q-t$ over $K=\mathbb{F}_r(t…