{
  "id": "2302.08350",
  "version": "v1",
  "published": "2023-02-16T15:11:23.000Z",
  "updated": "2023-02-16T15:11:23.000Z",
  "title": "Towards strong uniformity for isogenies of prime degree",
  "authors": [
    "Barinder S. Banwait",
    "Maarten Derickx"
  ],
  "comment": "19 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve over a number field $k$ of degree $d$ that admits a $k$-rational isogeny of prime degree $p$. We study the question of finding a uniform bound on $p$ that depends only on $d$, and obtain, under a certain condition on the signature of the isogeny, such a uniform bound by explicitly constructing nonzero integers that $p$ must divide. As a corollary we find a uniform bound on torsion points defined over unramified extensions of the base field, generalising Merel's Uniform Boundedness result for torsion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-16T15:11:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11Y60",
      "11G15"
    ],
    "keywords": [
      "prime degree",
      "strong uniformity",
      "generalising merels uniform boundedness result",
      "elliptic curve",
      "rational isogeny"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}