{
  "abstract": "Let $E/\\mathbb{Q}$ be a rational elliptic curve whose torsion group grows over a quadratic field $K$. In a previous paper, a relation between the primes of the conductor of $E$ and the primes that divide the discriminant of $K$ was shown. In the present paper, we go further in this study and we compute the ramification of the field $K$, when a torsion point of prime order $\\ell$ is added, in terms of invariants of the curve. Concretely, the conductor, the prime $\\ell$ and the Kodaira symbol at the primes of bad reduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01485",
  "author_total": 1,
  "authors": [
    {
      "name": "Miguel Pineda-Martín"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0fd3fqje927p3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01485",
  "fulltext_url": null,
  "id": "0fd3fqje927p3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01485",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7206193434",
  "pdf_url": "https://arxiv.org/pdf/2609.01485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0fd3fqje927p3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Ramification of Quadratic Fields where there is a torsion growth",
  "title_text": "On the Ramification of Quadratic Fields where there is a torsion growth",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/0fd3fqje927p3",
  "venue": "arXiv",
  "versions": []
}