{
  "id": "1403.7557",
  "version": "v2",
  "published": "2014-03-28T22:21:00.000Z",
  "updated": "2014-05-25T12:44:33.000Z",
  "title": "Explicit Families Of Elliptic Curves With The Same Mod 6 Representation",
  "authors": [
    "Zexiang Chen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve over $\\mathbb{Q}$. In this paper we study two certain modular curves which parameterize families of elliptic curves which are directly (resp. reverse) 6-congruent to $E$ together with the explicit parametrizations. The equations for the direct case has been worked out but the parametrization is only given for very few cases. In this paper we use a new method to obtain the equations for both direct and reverse cases together with full (and simpler) parametrizations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-25T12:44:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic curve",
      "explicit families",
      "representation",
      "explicit parametrizations",
      "direct case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.7557C"
    }
  }
}