{
  "abstract": "Let $E:y^2=x^3-x$. We prove that $\\#E(\\mathbf{F}_p)/8$ is squarefree and has at most two prime factors for $\\gg X/(\\log X)^2$ primes $p\\le X$. The proof follows the Gaussian CM sieve framework of Iwaniec and Jiménez Urroz and incorporates the intersection terms identified by Xie. For a squarefree Gaussian ideal $\\mathfrak{a}$, we separate its largest rational ideal factor and use the resulting divisibility of both integral coordinates to control the large-factor tail. This transfers an ideal Bombieri--Vinogradov estimate to rational norm divisibility at level $1/2$, with any fixed power of the divisor function as a weight. We prove the corresponding distribution estimate for the switched product sequence and apply the transfer to both sequences in Chen's weighted sieve. The primes counted may be restricted to $p\\equiv5\\pmod8$; their normalized orders are odd, squarefree, and supported on primes congruent to $1\\pmod4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20010",
  "author_total": 1,
  "authors": [
    {
      "name": "SeungJu Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bc2sdnaf6yekm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20010",
  "fulltext_url": null,
  "id": "bc2sdnaf6yekm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20010",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7222033702",
  "pdf_url": "https://arxiv.org/pdf/2610.20010",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bc2sdnaf6yekm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20010",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20010"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve",
  "title_text": "Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/bc2sdnaf6yekm",
  "venue": "arXiv",
  "versions": []
}