{
  "abstract": "We solve Conjecture 1.6 of Furio and Lombardo [On $7$-adic Galois representations for elliptic curves over $\\Q$, Proc.\\ London Math.\\ Soc.\\ (3) \\textbf{133} (2026), e70193.]. As a consequence, we complete the classification of $7$-adic Galois images for non-CM elliptic curves over $\\Q$. This is the first solved case in Problem 6.2 from Balakrishnan [\\emph{Chabauty and beyond: Explicit p-adic methods for rational points}, Proceedings of the International Congress of Mathematicians 2026 - Volume 3: Invited Lectures (Sections 1-4), 321-341, 2026]. The proof is the result of a long AI-training period by the author from June 2026 to September 2026. The author has been working on this project alone without the help of any other.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35460",
  "author_total": 1,
  "authors": [
    {
      "name": "Tho Nguyen Xuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3anvke6wzetga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35460",
  "fulltext_url": null,
  "id": "3anvke6wzetga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35460",
  "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": "W7214766584",
  "pdf_url": "https://arxiv.org/pdf/2609.35460",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3anvke6wzetga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35460",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35460"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Complete classification of $7$-adic Galois images for non-CM elliptic curves over $\\Q$",
  "title_text": "Complete classification of $7$-adic Galois images for non-CM elliptic curves over Q",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3anvke6wzetga",
  "venue": "arXiv",
  "versions": []
}