{
  "id": "1712.04214",
  "version": "v1",
  "published": "2017-12-12T10:28:52.000Z",
  "updated": "2017-12-12T10:28:52.000Z",
  "title": "Explicit Small Heights in Infinite Non-Abelian Extensions",
  "authors": [
    "Linda Frey"
  ],
  "comment": "23 pages, comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve over the rationals. We will consider the infinite extension $\\mathbb{Q}(E_{\\text{tor}})$ of the rationals where we adjoin all coordinates of torsion points of $E$. In this paper we will prove an explicit lower bound for the height of non-zero elements in $\\mathbb{Q}(E_{\\text{tor}})$ that are not a root of unity, only depending on the conductor of the elliptic curve. As a side result we will give an explicit bound for a small supersingular prime for an elliptic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-12T10:28:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G50"
    ],
    "keywords": [
      "explicit small heights",
      "infinite non-abelian extensions",
      "elliptic curve",
      "explicit lower bound",
      "small supersingular prime"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}