{
  "abstract": "We exhibit new subgroups of rational torsion points in geometrically simple Jacobians of genus-two curves over $\\mathbb Q$. The largest group, which has order 96 and invariants [2,2,2,12], is realized by curves of the form $y^2 = x(x-a^2)(x-b^2)(x-c^2)(x-u^2)(x-v^2)$ where $a,b,c,u,v$ are positive integers that satisfy $a^2 + b^2 + c^2 = u^2 + v^2$ and $a^4 + b^4 + c^4 = u^4 + v^4$. We also find realizations of the groups [2,2,20], [2,2,4,4], [2,2,2,8], [2,4,8], and [6,6]. Finally, we record, to the best of our knowledge, all known subgroups that arise in genus-two Jacobians over $\\mathbb Q$, in the geometrically simple case and in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28543",
  "author_total": 4,
  "authors": [
    {
      "name": "Jennifer S. Balakrishnan"
    },
    {
      "name": "Filip Najman"
    },
    {
      "name": "Ari Shnidman"
    },
    {
      "name": "Andrew V. Sutherland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/455x50basqdg7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28543",
  "fulltext_url": null,
  "id": "455x50basqdg7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28543",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204789477",
  "pdf_url": "https://arxiv.org/pdf/2608.28543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/455x50basqdg7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.28543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rational torsion on simple genus two Jacobians",
  "title_text": "Rational torsion on simple genus two Jacobians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/455x50basqdg7",
  "venue": "arXiv",
  "versions": []
}