{
  "id": "math/0510001",
  "version": "v1",
  "published": "2005-09-30T18:17:45.000Z",
  "updated": "2005-09-30T18:17:45.000Z",
  "title": "Note on the rank of quadratic twists of Mordell equations",
  "authors": [
    "Sungkon Chang"
  ],
  "comment": "8 pages; accepted by J. Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "14H52 : Elliptic curves Let E be the elliptic curve given by a Mordell equation y^2=x^3-A where A is an integer. For certain A, we use Stoll's formula to compute a lower bound for the proportion of square-free integers D up to X such that the Mordell-Weil rank of the quadratic twist by D is less than 2k, for given non-negative k. We also compute an upper bound for a certain average rank of quadratic twists of E.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-30T18:17:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52"
    ],
    "keywords": [
      "quadratic twist",
      "mordell equation",
      "elliptic curve",
      "average rank",
      "stolls formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10001C"
    }
  }
}