{
  "id": "0909.1614",
  "version": "v1",
  "published": "2009-09-09T02:52:51.000Z",
  "updated": "2009-09-09T02:52:51.000Z",
  "title": "On the Rank of the Elliptic Curve y^2=x(x-p)(x-2)",
  "authors": [
    "Jeffrey Hatley"
  ],
  "comment": "16 pages, lots of exposition",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "An elliptic curve E defined over \\Q is an algebraic variety which forms a finitely generated abelian group, and the structure theorem then implies that E = \\Z^r + \\Z_{tors} for some r \\geq 0; this value r is called the rank of E. It is a classical problem in the study of elliptic curves to classify curves by their rank. In this paper, the author uses the method of 2-descent to calculate the rank of two families of elliptic curves, where E is given by E: y^2 = x(x-p)(x-2) with p, p-2 being twin primes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-09T02:52:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14H52"
    ],
    "keywords": [
      "elliptic curve",
      "twin primes",
      "algebraic variety",
      "structure theorem",
      "finitely generated abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1614H"
    }
  }
}