{
  "id": "1611.05671",
  "version": "v1",
  "published": "2016-11-17T13:11:54.000Z",
  "updated": "2016-11-17T13:11:54.000Z",
  "title": "On a special case of Watkins' conjecture",
  "authors": [
    "Matija Kazalicki",
    "Daniel Kohen"
  ],
  "comment": "6 pages; comments are welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Watkins' conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper we prove that if the modular degree is odd then $E$ has rank $0$. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-17T13:11:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11F67"
    ],
    "keywords": [
      "special case",
      "rational elliptic curve",
      "conjecture asserts",
      "prime conductor",
      "modular parametrization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}