{
  "abstract": "Let $E$ be an elliptic curve defined over rational numbers. Further assume $E$ has good ordinary reduction at $p=2$ and $E[4]$ is reducible as a $G_\\mathbb{Q}$-representation. In this paper, we offer sufficient and necessary computational criteria for the algebraic Iwasawa $μ$-invariant over the cyclotomic $\\mathbb{Z}_2$-extension of rational number to be $0$, $1$ or $\\geq 2$. We also show that elliptic curves with isomorphic mod-$4$ representations have algebraic $μ$-invariant equal to $0$ if one of the curves does.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31532",
  "author_total": 2,
  "authors": [
    {
      "name": "Zichao Lin"
    },
    {
      "name": "Mulun Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5phax1x6hzmhp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31532",
  "fulltext_url": null,
  "id": "5phax1x6hzmhp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31532",
  "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",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7214622366",
  "pdf_url": "https://arxiv.org/pdf/2609.31532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5phax1x6hzmhp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Computing the Iwasawa $μ$-Invariants for Elliptic Curves over $\\mathbb{Z}_2$-Extensions",
  "title_text": "Computing the Iwasawa μ-Invariants for Elliptic Curves over ℤ_2-Extensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5phax1x6hzmhp",
  "venue": "arXiv",
  "versions": []
}