{
  "id": "2003.01253",
  "version": "v1",
  "published": "2020-03-02T23:47:35.000Z",
  "updated": "2020-03-02T23:47:35.000Z",
  "title": "The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal",
  "authors": [
    "Alina Carmen Cojocaru",
    "Matthew Fitzpatrick"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E/\\mathbb{Q}$ be a non-CM elliptic curve. Assuming GRH, we prove that, for a set of primes $p$ of density $1$, the absolute discriminant of the $\\mathbb{F}_p$-endomorphism ring of the reduction of $E$ modulo $p$ is close to maximal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-02T23:47:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G20",
      "11N05",
      "11N36",
      "11N37",
      "11N57"
    ],
    "keywords": [
      "non-cm elliptic curve",
      "absolute discriminant",
      "endomorphism ring",
      "assuming grh"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}