{
  "id": "0901.0120",
  "version": "v3",
  "published": "2008-12-31T17:11:04.000Z",
  "updated": "2009-09-08T14:40:44.000Z",
  "title": "On a theorem of Mestre and Schoof",
  "authors": [
    "John E. Cremona",
    "Andrew V. Sutherland"
  ],
  "comment": "6 pages, to appear in Journal de Th\\'eorie des Nombres de Bordeaux",
  "journal": "Journal de Th\\'eorie des Nombres de Bordeaux 22 (2010), 353-358",
  "doi": "10.5802/jtnb.719",
  "categories": [
    "math.NT"
  ],
  "abstract": "A well known theorem of Mestre and Schoof implies that the order of an elliptic curve E over a prime field F_q can be uniquely determined by computing the orders of a few points on E and its quadratic twist, provided that q > 229. We extend this result to all finite fields with q > 49, and all prime fields with q > 29.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-09-08T14:40:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20"
    ],
    "keywords": [
      "prime field",
      "finite fields",
      "elliptic curve",
      "schoof implies"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0120C"
    }
  }
}