{
  "id": "1808.02887",
  "version": "v1",
  "published": "2018-08-08T13:40:04.000Z",
  "updated": "2018-08-08T13:40:04.000Z",
  "title": "On the torsion of rational elliptic curves over sextic fields",
  "authors": [
    "Harris B. Daniels",
    "Enrique González-Jiménez"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Given an elliptic curve $E/\\mathbb{Q}$ with torsion subgroup $G = E(\\mathbb{Q})_{\\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\\mathbb{Q}$. We also determine which groups $H = E(K)_{\\rm tors}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-08T13:40:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14H52",
      "14G05"
    ],
    "keywords": [
      "rational elliptic curves",
      "sextic fields",
      "torsion subgroup",
      "first step",
      "complete classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}