{
  "id": "1006.1782",
  "version": "v4",
  "published": "2010-06-09T12:18:20.000Z",
  "updated": "2011-11-02T00:36:26.000Z",
  "title": "A local-global principle for rational isogenies of prime degree",
  "authors": [
    "Andrew V. Sutherland"
  ],
  "comment": "11 pages, minor edits, to appear in Journal de Th\\'eorie des Nombres de Bordeaux",
  "journal": "Journal de Th\\'eorie des Nombres de Bordeaux 24 (2012), 475-485",
  "doi": "10.5802/jtnb.807",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let K be a number field. We consider a local-global principle for elliptic curves E/K that admit (or do not admit) a rational isogeny of prime degree n. For suitable K (including K=Q), we prove that this principle holds when n = 1 mod 4, and for n < 7, but find a counterexample when n = 7 for an elliptic curve with j-invariant 2268945/128. For K = Q we show that, up to isomorphism, this is the only counterexample.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-11-02T00:36:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05"
    ],
    "keywords": [
      "prime degree",
      "rational isogeny",
      "local-global principle",
      "elliptic curves e/k",
      "number field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1782S"
    }
  }
}