{
  "id": "1212.5350",
  "version": "v2",
  "published": "2012-12-21T07:19:59.000Z",
  "updated": "2017-01-13T04:25:02.000Z",
  "title": "On the elliptic curve $ y^{2} = x (x^2 + p)$ over some certain imaginary quadratic fields",
  "authors": [
    "Xiumei Li"
  ],
  "comment": "this paper has been withdrawn by the author due to a crucial sign error",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we will talk about the titled elliptic curve defined over imaginary quadratic fields such as $\\mathbb{Q}(\\sqrt{-q})$, where $q$ is congruent to 3 modulo 8 and $(p,q)=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-21T07:19:59.000Z",
      "abstract": "In this paper, we will talk about the titled elliptic curve defined over imaginary quadratic fields such as $K=\\mathbb{Q}(\\sqrt{-1}), \\mathbb{Q}(\\sqrt{-2}), \\mathbb{Q}(\\sqrt{-7}), \\mathbb{Q}(\\sqrt{-q})$, where $q$ is congruent to 3 modulo 8 and $(p,q)=1$.",
      "comment": "22",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-01-13T04:25:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "11G05"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "titled elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5350L"
    }
  }
}