Elliptic Curves with Isomorphic Groups of Points over Finite Field Extensions

Clemens Heuberger, Michela Mazzoli

Consider a pair of ordinary elliptic curves $E$ and $E^{\prime }$ defined over the same finite field ${\mathbb{F}}_q$. Suppose they have the same number of ${\mathbb{F}}_q$-rational points, i.e…