{
  "abstract": "We determine thirteen entirely CM identity fibers of Shimura parametrizations attached to elliptic curves of rank two and conductor below $2000$. Each yields a proof of the imaginary quadratic class number one theorem. The argument combines the Gross--Zagier formula with the Ribet--Takahashi degree comparison to show that the fiber is completely explained by known CM points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16953",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingxuan Geng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e6b89rqy1vv7r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16953",
  "fulltext_url": null,
  "id": "e6b89rqy1vv7r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16953",
  "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.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221817407",
  "pdf_url": "https://arxiv.org/pdf/2610.16953",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e6b89rqy1vv7r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16953",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16953"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "CM fibers of Shimura parametrizations and thirteen proofs of the class number one theorem",
  "title_text": "CM fibers of Shimura parametrizations and thirteen proofs of the class number one theorem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/e6b89rqy1vv7r",
  "venue": "arXiv",
  "versions": []
}