Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$

Abraham Zhang

Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$

Number Theory 2026-07-24 v1

Authors: Abraham Zhang

Abstract

We improve an explicit upper bound on the modular polynomial $\Phi_N$ given by Breuer, G\'omez, 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 $\mathfrak f$ .

Cite

@article{arxiv.2607.22214,
  title  = {Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$},
  author = {Abraham Zhang},
  journal= {arXiv preprint arXiv:2607.22214},
  year   = {2026}
}

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16 pages, 0 figures