{
  "id": "1609.05312",
  "version": "v1",
  "published": "2016-09-17T10:12:37.000Z",
  "updated": "2016-09-17T10:12:37.000Z",
  "title": "Mordell-Weil lattice of Inose's Elliptic $K3$ surface arising from the product of 3-isogenous elliptic curves",
  "authors": [
    "Masato Kuwata",
    "Kazuki Utsumi"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "From the product of two elliptic curves, Shioda and Inose constructed an elliptic $K3$ surface having two $\\mathrm{II}^*$ fibers. Its Mordell-Weil lattice structure depends on the morphisms between the two elliptic curves. In this paper, we give a method of writing down generators of the Mordell-Weil lattice of such elliptic surfaces when two elliptic curves are $3$-isogenous. In particular, we obtain a basis of the Mordell-Weil lattice for the singular $K3$ surfaces $X_{[3,3,3]}$, $X_{[3,2,3]}$ and $X_{[3,0,3]}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-17T10:12:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J27",
      "14J28",
      "14H52",
      "11G05"
    ],
    "keywords": [
      "elliptic curves",
      "inoses elliptic",
      "surface arising",
      "mordell-weil lattice structure",
      "elliptic surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}