{
  "id": "math/0105232",
  "version": "v1",
  "published": "2001-05-28T14:45:09.000Z",
  "updated": "2001-05-28T14:45:09.000Z",
  "title": "Modular Curves Of Genus 2",
  "authors": [
    "Enrique Gonzalez-Jimenez",
    "Josep Gonzalez"
  ],
  "journal": "Math. Comp. 72, no. 241, 397-418, (2003)",
  "doi": "10.1090/S0025-5718-02-01458-8",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove that there is only a finite number of genus 2 curves C defined over Q such that there exists a nonconstant morphism pi:X_1(N) --->C defined over Q and the jacobian of C, J(C), is a Q-factor of the new part of the jacobian of X_1(N), J_1(N)^{new}. Moreover, we prove that there are only 149 genus two curves of this kind with the additional requeriment that their jacobians are Q-simple. We determine the corresponding newforms and present equations for all these curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-05-28T14:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G35",
      "14H45",
      "11F11",
      "11G10"
    ],
    "keywords": [
      "modular curves",
      "finite number",
      "nonconstant morphism",
      "additional requeriment",
      "corresponding newforms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Math. Comp."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}