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arXiv · 2610.21488

Smoothness of Shortest Isogenies to Frobenius Conjugates

Yi Ouyang·Wei Wei·Zheng Xu
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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 $E^{(p)}$.

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Yi Ouyang, Wei Wei, Zheng Xu. 2026-10-25. Smoothness of Shortest Isogenies to Frobenius Conjugates. https://arxiv.org/abs/2610.21488

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