{
  "id": "1609.04715",
  "version": "v1",
  "published": "2016-09-15T16:09:25.000Z",
  "updated": "2016-09-15T16:09:25.000Z",
  "title": "Mordell-Weil ranks of families of elliptic curves parametrized by binary quadratic forms",
  "authors": [
    "Bartosz Naskręcki"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove results on the Mordell--Weil rank of elliptic curves $y^2=x(x-\\alpha a^2)(x-\\beta b^2)$ parametrized by binary quadratic forms $\\alpha a^2+\\beta b^2=\\gamma c^2$. We express our explicit lower bounds over number fields and offer a detailed description of the corresponding Mordell-Weil group structure in the function field case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-15T16:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "11D25",
      "11D45",
      "11G05"
    ],
    "keywords": [
      "binary quadratic forms",
      "mordell-weil rank",
      "elliptic curves",
      "explicit lower bounds",
      "function field case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}