{
  "id": "1306.1410",
  "version": "v1",
  "published": "2013-06-06T13:58:42.000Z",
  "updated": "2013-06-06T13:58:42.000Z",
  "title": "Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve",
  "authors": [
    "Tom Fisher",
    "Rachel Newton"
  ],
  "comment": "28 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-06T13:58:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G07",
      "16H05"
    ],
    "keywords": [
      "elliptic curve",
      "cassels-tate pairing",
      "significant modifications",
      "upper bound",
      "global parts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1410F"
    }
  }
}