{
  "id": "2110.07819",
  "version": "v2",
  "published": "2021-10-15T02:32:55.000Z",
  "updated": "2022-06-07T18:43:54.000Z",
  "title": "Torsion for CM elliptic curves defined over number fields of degree 2p",
  "authors": [
    "Abbey Bourdon",
    "Holly Paige Chaos"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For a prime number p, we characterize the groups that may arise as torsion subgroups of an elliptic curve with complex multiplication defined over a number field of degree 2p. In particular, our work shows that a classification in the strongest sense is tied to determining whether there exist infinitely many Sophie Germain primes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-06-07T18:43:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G15",
      "11G05"
    ],
    "keywords": [
      "cm elliptic curves",
      "degree 2p",
      "number field",
      "sophie germain primes",
      "complex multiplication"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}