Splitting of three in Q of square root minus p
= Splitting of three in Q of square root minus p
If $p\equiv11\pmod{12}$ and $K=\mathbb Q(\sqrt{-p})$, then $\mathcal O_K=\mathbb Z[(1+\sqrt{-p})/2]$. The generator's minimal polynomial reduces modulo $3$ to $T(T-1)$, so $(3)$ splits into two distinct prime ideals of norm three.