Hilbert class field

Question

I got this doubt after going through tables given by Henri Cohen: Advanced topics in Computational number theory on "Hilbert Class Field of Imaginary quadratic field". pg no.539-542, sec 12.1 and a Book by D A Cox on Primes of the form $x^2+n y^2$. In Cox Book, Hilbert Class field of $K=Q(\sqrt{-14})$ is computed as $L=K(\alpha)$, where $\alpha=\sqrt{2\sqrt{2}-1}$ and in Cohen's book, the Hilbert Class field of imaginary quadratic field with discriminant $-56$ is calculated as $X^4-X^3+X+1$, so how these two are equal