{
  "id": "1805.05862",
  "version": "v1",
  "published": "2018-05-15T15:52:54.000Z",
  "updated": "2018-05-15T15:52:54.000Z",
  "title": "The Birch and Swinnerton-Dyer conjecture for an elliptic curve over $\\mathbb{Q}(\\sqrt[4]{5})$",
  "authors": [
    "Raymond van Bommel"
  ],
  "comment": "10 pages, all comments are appreciated!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we show the Birch and Swinnerton-Dyer conjecture for a certain elliptic curve over $\\mathbb{Q}(\\sqrt[4]{5})$ is equivalent to the same conjecture for a certain pair of hyperelliptic curves of genus 2 over $\\mathbb{Q}$. We numerically verify the conjecture for these hyperelliptic curves. Moreover, we explain the methods used to find this example, which turned out to be a bit more subtle than expected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-15T15:52:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40",
      "11G10",
      "11G30",
      "14K02"
    ],
    "keywords": [
      "swinnerton-dyer conjecture",
      "hyperelliptic curves",
      "equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}