{
  "abstract": "We record a finite-field census of the split-cubic elliptic curves $E_{a,b,c}^{(n)}:y^2=(ax+n)(bx+n)(cx+n)$ attached to positive integral $D(n)$-triples. For $n\\in\\{-3,3,5,8,12,20\\}$ there are $164$ such triples with $1\\le a<b<c\\le100$, allowing zero squares. Their reductions at the ten primes $\\operatorname{NextPrime}(10^k)$, $3\\le k\\le12$, give $1640$ records, of which $45$ have cofactor four relative to the largest prime divisor of the group order. We collect the standard split-cubic and quadratic-twist identities in the explicit normalization $λ=b(c-a)/(c(b-a))$ and $δ=cn(b-a)$, and use them to audit the point counts. The archive records group orders, factorizations, cofactors, embedding degrees and transfer-field bit lengths. A worked example compares the main curve with its nonsquare twist. The census is deterministic and descriptive; it provides neither an asymptotic density estimate nor cryptographic parameter recommendations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03121",
  "author_total": 4,
  "authors": [
    {
      "name": "Sompong Chuysurichay"
    },
    {
      "name": "Sawian Jaidee"
    },
    {
      "name": "Chatchawan Panraksa"
    },
    {
      "name": "Teerapol Sukhonwimolmal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmk81rkjbes09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03121",
  "fulltext_url": null,
  "id": "fmk81rkjbes09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03121",
  "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": "W7220448556",
  "pdf_url": "https://arxiv.org/pdf/2610.03121",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmk81rkjbes09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03121",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03121"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census",
  "title_text": "Split-Cubic Curves from D(n)-Triples: A Bounded Finite-Field Census",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/fmk81rkjbes09",
  "venue": "arXiv",
  "versions": []
}