The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I

John Cullinan, Nathan Kaplan

Let $\ell$ be a prime number and let $E$ and $E^{\prime }$ be $\ell$-isogenous elliptic curves defined over a finite field $k$ of characteristic $p\ne \ell$. Suppose the groups $E(k)$ and…