Exact counts of elliptic curves of bounded height over ${\mathbb{F}}_q(t)$ in characteristics $2$ and $3$

Jun-Yong Park

Let $p\in \{2,3\}$, let $q=p^r$ with $r\ge 1$, and put $K={\mathbb{F}}_q(t)$. We determine the exact weighted and unweighted counts of $K$-isomorphism classes of elliptic curves of bou…