{
  "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 $E^{(p)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21488",
  "author_total": 3,
  "authors": [
    {
      "name": "Yi Ouyang"
    },
    {
      "name": "Wei Wei"
    },
    {
      "name": "Zheng Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ng54hvdtvgvy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21488",
  "fulltext_url": null,
  "id": "3ng54hvdtvgvy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21488",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CR"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222409005",
  "pdf_url": "https://arxiv.org/pdf/2610.21488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ng54hvdtvgvy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.21488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Smoothness of Shortest Isogenies to Frobenius Conjugates",
  "title_text": "Smoothness of Shortest Isogenies to Frobenius Conjugates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3ng54hvdtvgvy",
  "venue": "arXiv",
  "versions": []
}