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

Abraham Zhang

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arXiv · 2607.22214

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

Abraham Zhang

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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 $\mathfrak f$.

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Abraham Zhang. 2026-07-24. Explicit height bounds on modular polynomials for the elliptic $j$-invariant, cube root of $j$, and Weber modular function $\mathfrak f$. https://arxiv.org/abs/2607.22214

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