{
  "id": "math/0210391",
  "version": "v1",
  "published": "2002-10-24T17:59:25.000Z",
  "updated": "2002-10-24T17:59:25.000Z",
  "title": "Belyi parametrisations of elliptic curves and congruence defects",
  "authors": [
    "Chandrashekhar Khare"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note we consider questions about parametrisations of elliptic curves defined over number fields by quotients of the upper half-plane by finite index subgroups of SL_2(Z). We ask if we can choose such a parametrisation of an elliptic curve to reflect the field over which it is defined: this can be viewed as a generalisation of the Shimura-Taniyama-Weil conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-24T17:59:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "congruence defects",
      "belyi parametrisations",
      "finite index subgroups",
      "number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10391K"
    }
  }
}