{
  "abstract": "We investigate the extent to which the coefficients $(w_1,w_2,w_3,w_4,w_6)$ of the reduced minimal Weierstrass model of an elliptic curve $E/\\mathbb{Q}$ are determined by the Dirichlet coefficients $a_n(E)$ of its $L$-function, whose values at primes of good reduction are the Frobenius traces of $E$. We prove that $w_1$, $w_2$ and $w_3$ are given by explicit formulae in $a_2(E)$, $a_3(E)$ and $a_4(E)$, that $w_4$ modulo $5$ is then determined by $a_5(E)$, and that $w_6$ modulo $7$ is determined by $a_7(E)$ together with $w_1,w_2,w_3,w_4$. These formulae, which appear to be new, were discovered by training decision tree models on the LMFDB; we report the accompanying experiments and explore applications to computing tables of elliptic curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24251",
  "author_total": 6,
  "authors": [
    {
      "name": "Barinder S. Banwait"
    },
    {
      "name": "Xiaoyu Huang"
    },
    {
      "name": "Kyu-Hwan Lee"
    },
    {
      "name": "Seewoo Lee"
    },
    {
      "name": "Thomas Oliver"
    },
    {
      "name": "Alexey Pozdnyakov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e18yphm6z9s5k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24251",
  "fulltext_url": null,
  "id": "e18yphm6z9s5k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24251",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7171556988",
  "pdf_url": "https://arxiv.org/pdf/2607.24251",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e18yphm6z9s5k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2607.24251",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24251"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves",
  "title_text": "Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/e18yphm6z9s5k",
  "venue": "arXiv",
  "versions": []
}