Factorization of Hilbert class polynomials over prime fields

Jianing Li, Songsong Li, Yi Ouyang

Let $D$ be a negative integer congruent to $0$ or $1\mathrm{mod}4$ and $\mathcal{O}={\mathcal{O}}_D$ be the corresponding order of $K=\mathbb{Q}(\sqrt{D})$. The Hilbert class polynomial…