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

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 $\mathfrak f$.