Ideal class group of Q square root of minus fourteen
= Ideal class group of Q square root of minus fourteen
{title2=$\operatorname{Cl}(\mathbb Q(\sqrt{-14}))\cong C_4$}
In $K=\mathbb Q(\sqrt{-14})$, the <Minkowski bound for ideal classes> is less than five. The <ideals> $\mathfrak p=(2,\sqrt{-14})$ and $\mathfrak q=(3,1+\sqrt{-14})$ generate all classes, with $\mathfrak p^2=(2)$ and $(2-\sqrt{-14})=\mathfrak p\mathfrak q^2$. No element has <field norm> two, so $[\mathfrak p]$ has order two and $[\mathfrak q]$ has order four.