{
  "abstract": "Let $E/\\Q$ be an elliptic curve and let $\\widetilde K_p$ be the compositum of all $\\Z_p$-extensions of a quadratic field $K$. We prove that $E(\\widetilde K_p)_{\\tors}=E(K)_{\\tors}$ for $p\\geq5$. For $p=3$ and imaginary quadratic $K\\neq\\Q(\\sqrt{-3})$, torsion on each extension is determined by its intersections with the cyclotomic extension and the $2$-division field. Over $\\Q(\\sqrt{-3})$, we construct infinitely many non-CM curves with full $3$-torsion in the first anticyclotomic layer and compute the $3$-primary torsion on every slope for eight CM curves. For $p=2$, we bound the odd-primary torsion and exclude all primes greater than $7$. We also give uniform bounds for non-CM primary torsion and correct two assertions in Li's preprint about noncyclotomic $\\Z_3$-extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.17303",
  "author_total": 2,
  "authors": [
    {
      "name": "Shisong Xu"
    },
    {
      "name": "Haoyang Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bdmqhp6njcx14.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.17303",
  "fulltext_url": null,
  "id": "bdmqhp6njcx14",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.17303",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7169860421",
  "pdf_url": "https://arxiv.org/pdf/2607.17303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bdmqhp6njcx14.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2607.17303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.17303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Torsion growth of rational elliptic curves over $\\Z_p$-extensions of quadratic fields",
  "title_text": "Torsion growth of rational elliptic curves over Z_p-extensions of quadratic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/bdmqhp6njcx14",
  "venue": "arXiv",
  "versions": []
}