Smoothness of Shortest Isogenies to Frobenius Conjugates

arXiv:2610.21488v1 Announce Type: cross Abstract: Let $E$ be chosen uniformly from the geometric isomorphism classes of supersingular elliptic curves over $\overline{\mathbb{F}}_p$ and $\delta_E$ be the minimum degree of isogenies from $E$ to its Frobenius conjugate $E^{(p)}$. We prove the smoothness of $\delta_E$ and hence affirm Wesolowski's $p^{1/3+o(1)}$ attack on the supersingular endomorphism ring problem is unconditional.