{
  "abstract": "We study the Iwasawa $μ$- and $λ$-invariants of quadratic twists of rational elliptic curves at Eisenstein primes $p\\geq 3$. We verify Greenberg's $μ=0$ conjecture for all such twists, which gives an Euler system free proof of Mazur's cotorsion conjecture, and study the $λ$-invariants when the twist is admissible in the sense of [GV00]. As a consequence, we prove the cyclotomic Iwasawa Main Conjecture and obtain the $p$-part BSD formulae in rank $0$ for admissible twists under mild conditions, covering many elliptic curves of potentially ordinary reduction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42137",
  "author_total": 1,
  "authors": [
    {
      "name": "Mulun Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b36pfyr6sz9vd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42137",
  "fulltext_url": null,
  "id": "b36pfyr6sz9vd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42137",
  "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/2610.42137",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b36pfyr6sz9vd.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42137",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42137"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primes",
  "title_text": "On the Iwasawa invariants of admissible quadratic twists of elliptic curves at ordinary Eisenstein primes",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/b36pfyr6sz9vd",
  "venue": "arXiv",
  "versions": []
}