{
  "id": "0706.4379",
  "version": "v1",
  "published": "2007-06-29T09:46:35.000Z",
  "updated": "2007-06-29T09:46:35.000Z",
  "title": "Quartic equations and 2-division on elliptic curves",
  "authors": [
    "George H. Hitching"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let K be a field of characteristic different from 2 and C an elliptic curve over K given by a Weierstrass equation. To divide an element of the group C by 2, one must solve a certain quartic equation. We characterise the quartics arising from this procedure and find how far the quartic determines the curve and the point. We find the quartics coming from 2-division of 2- and 3-torsion points, and generalise this correspondence to singular plane cubics. We use these results to study the question of which degree 4 maps of curves can be realised as duplication of a multisection on an elliptic surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-29T09:46:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H52",
      "14J27"
    ],
    "keywords": [
      "elliptic curve",
      "quartic equation",
      "singular plane cubics",
      "weierstrass equation",
      "elliptic surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4379H"
    }
  }
}