Hilbert class field of $\mathbb Q(\sqrt{-39})$

Question

Is the Hilbert class field of $K=\mathbb Q\left(\sqrt{-39}\right)$ is equal to $K\left(\sqrt{-39},\frac{\sqrt{1+\sqrt{13}}}{2}\right)$

Answer 1

According to Lemmermayer's computation it is $\mathbb{Q}(\sqrt{-39},\sqrt{-2+2\sqrt{13}})$, see "Class field towers".