Year: 2026
Type: preprint
Abstract: Let $E$ be chosen uniformly from the geometric isomorphism classes of supersingular elliptic curves over $\overline{\mathbb{F}}_p$ and $δ_E$ be the minimum degree of isogenies from $E$ to its Frobenius conjugate $E^{(p)}$. We establish bounds for the smoothness probability of $δ_E$ and hence affirm Wesolowski's $p^{1/3+o(1)}$ attack on the supersingular endomorphism ring problem is unconditional. We also establish a uniform asymptotic formula, with a main term expressed in terms of Dirichlet $L$ values, for the probability that a connection isogeny of degree $n$ exists between $E$ and $E^{(p)}$.
Source: arXiv (Cornell University)
Authors: Ouyang, Yi, Wei, Wei, Xu, Zheng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222409005