{
  "id": "1912.07159",
  "version": "v1",
  "published": "2019-12-16T02:09:04.000Z",
  "updated": "2019-12-16T02:09:04.000Z",
  "title": "Torsion of rational elliptic curves over different types of cubic fields",
  "authors": [
    "Daeyeol Jeon",
    "Andreas Schweizer"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve defined over $\\Q$, and let $G$ be the torsion group $E(K)_{tors}$ for some cubic field $K$ which does not occur over $\\Q$. In this paper, we determine over which types of cubic number fields (cyclic cubic, non-Galois totally real cubic, complex cubic or pure cubic) $G$ can occur, and if so, whether it can occur infinitely often or not. Moreover, if it occurs, we provide elliptic curves $E/\\Q$ together with cubic fields $K$ so that $G= E(K)_{tors}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-16T02:09:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G18"
    ],
    "keywords": [
      "rational elliptic curves",
      "cubic field",
      "cubic number fields",
      "non-galois totally real cubic",
      "pure cubic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}