{
  "id": "1404.7738",
  "version": "v2",
  "published": "2014-04-30T14:33:25.000Z",
  "updated": "2014-05-27T14:18:38.000Z",
  "title": "Height of rational points on quadratic twists of a given elliptic curve",
  "authors": [
    "Pierre Le Boudec"
  ],
  "comment": "The results are now stated using (the exponential of) the canonical height. Thanks to Joe Silverman for enlightening comments on the previous version",
  "categories": [
    "math.NT"
  ],
  "abstract": "We formulate a conjecture about the distribution of the canonical height of the lowest non-torsion rational point on a quadratic twist of a given elliptic curve, as the twist varies. This conjecture seems to be very deep and we can only prove partial results in this direction.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-27T14:18:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D45",
      "11G05",
      "14G05"
    ],
    "keywords": [
      "elliptic curve",
      "quadratic twist",
      "lowest non-torsion rational point",
      "conjecture",
      "twist varies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.7738L"
    }
  }
}