{
  "id": "1202.0337",
  "version": "v1",
  "published": "2012-02-02T01:59:08.000Z",
  "updated": "2012-02-02T01:59:08.000Z",
  "title": "Elliptic Curves, eta-quotients, and hypergeometric functions",
  "authors": [
    "Eugene Yoong",
    "David Pathakjee",
    "Zef Rosnbrick"
  ],
  "comment": "Accepted for publication by journal Involve",
  "categories": [
    "math.NT"
  ],
  "abstract": "The well-known fact that all elliptic curves are modular, proven by Wiles, Taylor, Breuil, Conrad and Diamond, leaves open the question whether there exists a 'nice' representation of the modular form associated to each elliptic curve. Here we provide explicit representations of the modular forms associated to certain Legendre form elliptic curves 2_E_1({\\lambda}) as linear combinations of quotients of Dedekind's eta-function. We also give congruences for some of the modular forms' coefficients in terms of Gaussian hypergeometric functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-02T01:59:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular form",
      "eta-quotients",
      "legendre form elliptic curves",
      "gaussian hypergeometric functions",
      "leaves open"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0337Y"
    }
  }
}