{
  "id": "0706.3711",
  "version": "v4",
  "published": "2007-06-25T21:14:08.000Z",
  "updated": "2009-08-06T04:48:29.000Z",
  "title": "Point counting on reductions of CM elliptic curves",
  "authors": [
    "K. Rubin",
    "A. Silverberg"
  ],
  "comment": "Minor corrections. To appear in Journal of Number Theory",
  "doi": "10.1016/j.jnt.2009.01.020",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\\mathbf{Q}$-curves in certain cases. This generalizes earlier results of Gross, Stark, and others.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-08-06T04:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G15",
      "11G20"
    ],
    "keywords": [
      "cm elliptic curves",
      "point counting",
      "reductions",
      "imaginary quadratic field",
      "generalizes earlier results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.3711R"
    }
  }
}