{
  "id": "math/0604524",
  "version": "v1",
  "published": "2006-04-25T08:58:19.000Z",
  "updated": "2006-04-25T08:58:19.000Z",
  "title": "Deciding existence of rational points on curves: an experiment",
  "authors": [
    "Nils Bruin",
    "Michael Stoll"
  ],
  "comment": "12 pages",
  "journal": "Experiment. Math. 17 (2008), no. 2, 181--189.",
  "categories": [
    "math.NT"
  ],
  "abstract": "We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For each of these roughly 200000 isomorphism classes of curves, we decide if there is a rational point on the curve or not, by a combination of techniques. For a small number of curves, our result is conditional on the BSD conjecture or on GRH.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-25T08:58:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D41",
      "11G30",
      "11Y50",
      "14G05",
      "14G25",
      "14H25",
      "14H45",
      "14Q05"
    ],
    "keywords": [
      "rational point",
      "deciding existence",
      "experiment",
      "isomorphism classes",
      "squarefree polynomial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4524B"
    }
  }
}