Do Eon Cha

Double-orientations on supersingular isogeny graphs

We recall and define various kinds of supersingular $\ell$-isogeny graphs and precise graph isomorphism with a corresponding quaternion $\ell$-ideal graph. In particular, we introduce the notion of double-orientations on supersingular elliptic curves and study the structure of double-oriented supersingular $\ell$-isogeny graphs.