Explicit points on $y^2+xy-t^{d}y=x^3$ and related character sums

Christopher Davis, Tommy Occhipinti

Let ${\mathbb{F}}_q$ denote a finite field of characteristic $p\ge 5$ and let $d=q+1$. Let $E_d$ denote the elliptic curve over the function field ${\mathbb{F}}_{q^2}(t)$ defined b…