{
  "id": "math/0312285",
  "version": "v1",
  "published": "2003-12-15T03:15:00.000Z",
  "updated": "2003-12-15T03:15:00.000Z",
  "title": "Curves of genus 2 with (n, n)-decomposable jacobians",
  "authors": [
    "T. Shaska"
  ],
  "journal": "J. Symbolic Comp. 31 (2001), no. 5, 603-617",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be a curve of genus 2 and $\\psi_1:C \\lar E_1$ a map of degree $n$, from $C$ to an elliptic curve $E_1$, both curves defined over $\\bC$. This map induces a degree $n$ map $\\phi_1:\\bP^1 \\lar \\bP^1$ which we call a Frey-Kani covering. We determine all possible ramifications for $\\phi_1$. If $\\psi_1:C \\lar E_1$ is maximal then there exists a maximal map $\\psi_2:C\\lar E_2$, of degree $n$, to some elliptic curve $E_2$ such that there is an isogeny of degree $n^2$ from the Jacobian $J_C$ to $E_1 \\times E_2$. We say that $J_C$ is $(n,n)$-decomposable. If the degree $n$ is odd the pair $(\\psi_2, E_2)$ is canonically determined. For $n=3, 5$, and 7, we give arithmetic examples of curves whose Jacobians are $(n,n)$-decomposable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-15T03:15:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "arithmetic examples",
      "maximal map",
      "map induces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12285S"
    }
  }
}