{
  "id": "1701.06489",
  "version": "v1",
  "published": "2017-01-23T16:48:33.000Z",
  "updated": "2017-01-23T16:48:33.000Z",
  "title": "Plane quartics over Q with complex multiplication",
  "authors": [
    "Pinar Kilicer",
    "Hugo Labrande",
    "Reynald Lercier",
    "Christophe Ritzenthaler",
    "Jeroen Sijsling",
    "Marco Streng"
  ],
  "comment": "34 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give examples of smooth plane quartics over $Q$ with complex multiplication over $\\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-23T16:48:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex multiplication",
      "smooth plane quartics",
      "dixmier-ohno invariants",
      "maximal order",
      "fast computation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}