{
  "id": "1206.1585",
  "version": "v3",
  "published": "2012-06-07T19:27:10.000Z",
  "updated": "2014-02-11T21:26:17.000Z",
  "title": "A Cohen-Lenstra phenomenon for elliptic curves",
  "authors": [
    "Chantal David",
    "Ethan Smith"
  ],
  "comment": "A mistake was discovered in the derivation of the product formula for K(G). The included corrigendum corrects this mistake. All page numbers in the corrigendum refer to the journal version of the manuscript",
  "journal": "Journal of the London Mathematical Society, 89(1):24-44, 2014; Corrigendum: Journal of the London Mathematical Society, 89(1):45-46, 2014",
  "doi": "10.1112/jlms/jdt036 10.1112/jlms/jdu001",
  "categories": [
    "math.NT"
  ],
  "abstract": "Given an elliptic curve $E$ and a finite Abelian group $G$, we consider the problem of counting the number of primes $p$ for which the group of points modulo $p$ is isomorphic to $G$. Under a certain conjecture concerning the distribution of primes in short intervals, we obtain an asymptotic formula for this problem on average over a family of elliptic curves.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-02-11T21:26:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "cohen-lenstra phenomenon",
      "finite abelian group",
      "short intervals",
      "points modulo"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1585D"
    }
  }
}