{
  "id": "0802.2651",
  "version": "v2",
  "published": "2008-02-19T13:39:08.000Z",
  "updated": "2008-08-14T20:26:14.000Z",
  "title": "Multiples of integral points on elliptic curves",
  "authors": [
    "Patrick Ingram"
  ],
  "comment": "Revised version, correcting a significant error",
  "categories": [
    "math.NT"
  ],
  "abstract": "If $E$ is a minimal elliptic curve defined over $\\ZZ$, we obtain a bound $C$, depending only on the global Tamagawa number of $E$, such that for any point $P\\in E(\\QQ)$, $nP$ is integral for at most one value of $n>C$. As a corollary, we show that if $E/\\QQ$ is a fixed elliptic curve, then for all twists $E'$ of $E$ of sufficient height, and all torsion-free, rank-one subgroups $\\Gamma\\subseteq E'(\\QQ)$, $\\Gamma$ contains at most 6 integral points. Explicit computations for congruent number curves are included.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-08-14T20:26:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11K60"
    ],
    "keywords": [
      "integral points",
      "congruent number curves",
      "global tamagawa number",
      "explicit computations",
      "rank-one subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.2651I"
    }
  }
}