{
  "id": "math/0110262",
  "version": "v1",
  "published": "2001-10-24T05:31:31.000Z",
  "updated": "2001-10-24T05:31:31.000Z",
  "title": "On the group orders of elliptic curves over finite fields",
  "authors": [
    "Everett W. Howe"
  ],
  "comment": "18 pages, LaTeX. This is a preprint version from 1992",
  "journal": "Compositio Math. 85 (1993) 229--247",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves over F_q along with F_q-defined points P and Q of order m and n, respectively, with P and (n/m)Q having a given Weil pairing. Using these curves, we estimate the number of elliptic curves over F_q that have a given integer N dividing the number of their F_q-defined points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-10-24T05:31:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14G15",
      "14H52"
    ],
    "keywords": [
      "finite fields",
      "group orders",
      "parametrizes elliptic curves",
      "prime power",
      "modular curve"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10262H"
    }
  }
}