Yves Aubry

Minimal degree of an isogeny between a supersingular elliptic curve and its conjugate

Let $E$ be a supersingular elliptic curve defined over $\bar{\mathbb{F}}_p$ and $E^{(p)}$ be its conjugate. We give a bound on the minimal degree of an isogeny from $E$ to $E^{(p)}$ depending on $p$, and show that this bound is both asymptotically optimal as well as sharp in many cases. This bound is obtained by develo...