{
  "abstract": "We determine all the groups that appear as the torsion group of an elliptic curve over a number field of degree $6$. Apart from the $44$ groups that occur infinitely often, which were determined by Derickx and Sutherland, exactly four groups occur: $\\mathbb{Z}/25\\mathbb{Z}$, $\\mathbb{Z}/37\\mathbb{Z}$, $\\mathbb{Z}/4\\mathbb{Z}\\times\\mathbb{Z}/12\\mathbb{Z}$ and $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/24\\mathbb{Z}$. The first three were known to occur, while the group $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/24\\mathbb{Z}$ is new. We also show that, up to isomorphism, each of the groups $\\mathbb{Z}/37\\mathbb{Z}$ and $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/24\\mathbb{Z}$ is the torsion group of a single elliptic curve over a single sextic field. The methods build on those developed by Derickx and Najman for quartic fields and by the author for quintic fields. Among the new ingredients are a formal immersion criterion at the prime $2$ which uses the Cartier operator, and arguments with several diamond operators and with cuspidal divisor classes on quotients of modular curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03933",
  "author_total": 1,
  "authors": [
    {
      "name": "Filip Najman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2p6wy8xc4h6bc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03933",
  "fulltext_url": null,
  "id": "2p6wy8xc4h6bc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03933",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03933",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2p6wy8xc4h6bc.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03933",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03933"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of torsion of elliptic curves over sextic fields",
  "title_text": "Classification of torsion of elliptic curves over sextic fields",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/2p6wy8xc4h6bc",
  "venue": "arXiv",
  "versions": []
}