How to convert roots of Weber polynomial to Hilbert class polynomial over modulo prime? Using any non square root discriminant $D$, we should be able to find the Weber class polynomial. How can I convert the roots of a Weber polynomial to a Hilbert class polynomial over modulo prime?
Let $j_w$ be the root of Weber polynomial $W_D(X)$ over $F_p$, then the root $(j_h)$ of Hilbert polynomial $H_D(X)$ over $F_p$ is given by

$$j_h=\frac{{(j_w^{24}-16)}^3}{{j_w}^{24}}$$