Endomorphism Rings of Supersingular Elliptic Curves and Ternary Quadratic Forms

Guanju Xiao, Zijian Zhou, Longjiang Qu

Let $c<3p/16$ be a prime or $c=1$. Let $E$ be a $\mathbb{Z}[\sqrt{-cp}]$-oriented supersingular elliptic curve defined over ${\mathbb{F}}_{p^2}$. There exists a $c$-isogeny from $E$…