{
  "id": "1806.05993",
  "version": "v1",
  "published": "2018-06-15T14:19:03.000Z",
  "updated": "2018-06-15T14:19:03.000Z",
  "title": "Torsion groups of elliptic curves over quadratic fields $\\mathbb{Q}(\\sqrt{d}),$ $0<d<100$",
  "authors": [
    "Antonela Trbović"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove results towards classifying the possible torsion subgroups of elliptic curves over quadratic fields $\\mathbb{Q}(\\sqrt{d})$, where $0<d<100$ is a square-free integer, and obtain a complete classification for 49 out of 60 such fields. Over the remaining 11 quadratic fields, we cannot rule out the possibility of the group $\\mathbb{Z}/16\\mathbb{Z}$ appearing as a torsion group of an elliptic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-15T14:19:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05"
    ],
    "keywords": [
      "quadratic fields",
      "elliptic curve",
      "torsion group",
      "square-free integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}