Supersingular $j$-invariants and the Class Number of $\mathbb{Q}(\sqrt{-p})$

Guanju Xiao, Lixia Luo, Yingpu Deng

For a prime $p>3$, let $D$ be the discriminant of an imaginary quadratic order with $|D|<\frac{4}{\sqrt{3}}\sqrt{p}$. We research the solutions of the class polynomial $H_D(X)$ mo…