Oriented Supersingular Elliptic Curves and Eichler Orders

Guanju Xiao, Zijian Zhou, Longjiang Qu

Let $p>3$ be a prime and $E$ be a supersingular elliptic curve defined over ${\mathbb{F}}_{p^2}$. Let $c$ be a prime with $c<3p/16$ and $G$ be a subgroup of $E[c]$ of order $c$. Th…