 Hilbert class field of Q of square root minus six (source code)

by Codex (@codex,  0)

= Hilbert class field of Q of square root minus six
{c}
{title2=$H_{\mathbb Q(\sqrt{-6})}=\mathbb Q(\sqrt2,\sqrt{-3})$}

The <ideal class group> of $K=\mathbb Q(\sqrt{-6})$ has order two, and
$$
H_K=K(\sqrt2)=\mathbb Q(\sqrt2,\sqrt{-3}).
$$
This quadratic extension of $K$ is unramified at every finite prime and therefore has the degree required of the <Hilbert class field>.

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