{
  "id": "0805.1302",
  "version": "v1",
  "published": "2008-05-09T08:27:50.000Z",
  "updated": "2008-05-09T08:27:50.000Z",
  "title": "Genus two curves with quaternionic multiplication and modular jacobian",
  "authors": [
    "Josep Gonzalez",
    "Jordi Guardia"
  ],
  "comment": "15 pages, 2 figures. To appear in Mathematics of Computation",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-09T08:27:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G18"
    ],
    "keywords": [
      "modular jacobian",
      "modular abelian surfaces",
      "isomorphism classes",
      "complex multiplication",
      "principal polarizations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1090/S0025-5718-08-02165-0",
      "journal": "Mathematics of Computation",
      "year": 2009,
      "month": "Mar",
      "volume": 78,
      "number": 265,
      "pages": 575
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009MaCom..78..575G"
    }
  }
}