{
  "id": "1001.0100",
  "version": "v1",
  "published": "2010-01-03T04:16:44.000Z",
  "updated": "2010-01-03T04:16:44.000Z",
  "title": "The quadratic character of 1+\\sqrt{2} and an elliptic curve",
  "authors": [
    "Yu Tsumura"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "When p is congruent to 1 mod 8, we have a criterion of the quadratic character of 1+\\sqrt{2}, which is related to the class number of \\Q(\\sqrt{-p}). In this paper, we obtain a similar criterion using an elliptic curve, which contrasts to the proof using algebraic number theory for the old one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-03T04:16:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "11E25"
    ],
    "keywords": [
      "elliptic curve",
      "quadratic character",
      "algebraic number theory",
      "class number",
      "similar criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}