{
  "id": "1504.00999",
  "version": "v1",
  "published": "2015-04-04T10:02:32.000Z",
  "updated": "2015-04-04T10:02:32.000Z",
  "title": "Parametrizing elliptic curves by modular units",
  "authors": [
    "François Brunault"
  ],
  "comment": "7 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is well-known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over $\\mathbf{Q}$ can be parametrized by modular units. This answers a question raised by Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves $E$ of conductor up to $1000$ parametrized by modular units supported in the rational torsion subgroup of $E$. Finally, we raise several open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-04T10:02:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F03",
      "11G05",
      "11G16",
      "14H52"
    ],
    "keywords": [
      "modular units",
      "parametrizing elliptic curves",
      "rational torsion subgroup",
      "rationals admits",
      "open questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150400999B"
    }
  }
}