{
  "id": "1303.5218",
  "version": "v2",
  "published": "2013-03-21T10:22:51.000Z",
  "updated": "2013-04-06T09:03:13.000Z",
  "title": "On the 2-part of the Birch-Swinnerton-Dyer conjecture for elliptic curves with complex multiplication",
  "authors": [
    "John Coates",
    "Minhyong Kim",
    "Zhibin Liang",
    "Chunlai Zhao"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Given an elliptic curve E over Q with complex multiplication having good reduction at 2, we investigate the 2-adic valuation of the algebraic part of the L-value at 1 for a family of quadratic twists. In particular, we prove a lower bound for this valuation in terms of the Tamagawa number in a form predicted by the conjecture of Birch and Swinnerton-Dyer.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-06T09:03:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40"
    ],
    "keywords": [
      "complex multiplication",
      "elliptic curve",
      "birch-swinnerton-dyer conjecture",
      "algebraic part",
      "quadratic twists"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5218C"
    }
  }
}