{
  "abstract": "We improve an explicit upper bound on the height of the modular polynomial $Φ_N$ given by Breuer, Gómez, and Pazuki. We also prove new explicit upper bounds on the height of modular polynomials for the cube root of $j$ and the Weber modular function $\\mathfrak f$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22214",
  "author_total": 1,
  "authors": [
    {
      "name": "Abraham Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/effdfakfvpzqz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22214",
  "fulltext_url": null,
  "id": "effdfakfvpzqz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22214",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7171442306",
  "pdf_url": "https://arxiv.org/pdf/2607.22214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/effdfakfvpzqz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.22214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\\mathfrak f$",
  "title_text": "Explicit height bounds on modular polynomials for the elliptic j-invariant, cube root of j, and Weber modular function f",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/effdfakfvpzqz",
  "venue": "arXiv",
  "versions": []
}