{
  "id": "math/0305064",
  "version": "v1",
  "published": "2003-05-04T14:28:42.000Z",
  "updated": "2003-05-04T14:28:42.000Z",
  "title": "Ordinary elliptic curves of high rank over $\\bar F_p(x)$ with constant j-invariant",
  "authors": [
    "Irene I. Bouw",
    "Claus Diem",
    "Jasper Scholten"
  ],
  "comment": "15 pages, 0 figures, LaTeX",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over $\\bar F_p(x)$ with arbitrary high rank and constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/ell Z)^*/<-1> (ell an odd prime) there exists a hyperelliptic curve over $\\bar F_p$ whose Jacobian is isogenous to a power of one ordinary elliptic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-04T14:28:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G20",
      "14H40",
      "14H52"
    ],
    "keywords": [
      "ordinary elliptic curve",
      "constant j-invariant",
      "odd prime",
      "artins primitive root conjecture",
      "arbitrary high rank"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5064B"
    }
  }
}