{
  "id": "1108.6069",
  "version": "v1",
  "published": "2011-08-30T20:13:44.000Z",
  "updated": "2011-08-30T20:13:44.000Z",
  "title": "Why is the Class Number of $\\Q(\\sqrt[3]{11})$ even?",
  "authors": [
    "Franz Lemmermeyer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-30T20:13:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "class number",
      "pure cubic number fields",
      "hilbert class fields",
      "elliptic curves",
      "quadratic unramified extensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.6069L"
    }
  }
}