{
  "id": "1211.2188",
  "version": "v4",
  "published": "2012-11-09T16:59:14.000Z",
  "updated": "2014-09-03T10:58:46.000Z",
  "title": "Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$",
  "authors": [
    "Filip Najman"
  ],
  "comment": "22 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We classify the possible torsion structures of rational elliptic curves over cubic fields. Along the way we find a previously unknown torsion structure over a cubic field, $\\Z /21 \\Z$, which corresponds to a sporadic point on $X_1(21)$ of degree 3, which is the lowest possible degree of a sporadic point on a modular curve $X_1(n)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-13T06:45:45.000Z",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-09-03T10:58:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G18"
    ],
    "keywords": [
      "rational elliptic curves",
      "sporadic point",
      "cubic field",
      "unknown torsion structure",
      "modular curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2188N"
    }
  }
}