{
  "id": "1109.6278",
  "version": "v4",
  "published": "2011-09-28T17:31:58.000Z",
  "updated": "2014-02-26T11:59:27.000Z",
  "title": "On the number of elliptic curves with prescribed isogeny or torsion group over number fields of prime degree",
  "authors": [
    "Filip Najman"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $p$ be a prime and $K$ a number field of degree $p$. We count the number of elliptic curves, up to $\\bar{K}$-isomorphism, having a prescribed property, where this property is either that the curve contains a fixed torsion group as a subgroup, or that it has an isogeny of prescribed degree.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-02-26T11:59:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "number field",
      "elliptic curves",
      "prime degree",
      "prescribed isogeny",
      "curve contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6278N"
    }
  }
}