{
  "id": "2406.15606",
  "version": "v1",
  "published": "2024-06-21T19:16:12.000Z",
  "updated": "2024-06-21T19:16:12.000Z",
  "title": "Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of $\\mathbb{Q}$",
  "authors": [
    "Omer Avci"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $E$ be an elliptic curve defined over $\\mathbb{Q}$. Let $p>3$ be a prime such that $p-1$ is not divisible by $3,4,5,7,11$. In this article we classify the groups that can arise as $E(\\mathbb{Q}(\\zeta_p))_{\\text{tors}}$ up to isomorphism. The method illustrates techniques for eliminating possible structures that can appear as a subgroup of $E(\\mathbb{Q}^{ab})_{\\text{tors}}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-21T19:16:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11R20",
      "14H52"
    ],
    "keywords": [
      "rational elliptic curves",
      "cyclotomic extensions",
      "method illustrates techniques",
      "isomorphism",
      "structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}