Is class number the always the degree of [Hilbert class field of discriminant $D:K=\mathbb{Q}(\sqrt{d})]$

Question

I was going through https://services.math.duke.edu/~schoen/discriminants.html where the minimal polynomial whose quotient over $K=\mathbb{Q}(\sqrt{d})$ is equal to the Hilbert class field for discriminants $-23,-31,-44,-59,etc$ is equal to the class number corresponding to the discriminant except for the case where discriminant is $-104$. Why is it not a degree $6$ polynomial?

I went through this code from Pg 47 https://static1.squarespace.com/static/5aff705c5ffd207cc87a512d/t/5bb78d47ec212d427af6dbd0/1538755912894/Class+Field+Theory.pdf but this runs perfectly for $D=-47$ but not for others. Here the degree of minimal polynomial corresponds to [Hilbert class field of discriminant $D: \mathbb{Q}]$.

And for the case of $D=-23$, the polynomial obtained is some random degree $3$ polynomial and does not match with the one on https://services.math.duke.edu/~schoen/discriminants.html

What is happening in this code? It does not even generate the correct answer for $-27$ or any other discriminant.

> R<x> := PolynomialRing(RationalField());
> K<a> := NumberField(x^2 + 47);
> ClassNumber(K);
> L<b> := HilbertClassField(K);
> f<x> := MinimalPolynomial(b,K);
> f;
>L; 

Answer 1

In magma, instead of

L<b> := HilberClassField(K);

try

L := HilberClassField(K); b := PrimitiveElement(L);

Then Degree(MinimalPolynomial(b,K)) is equal to ClassNumber(K) as told by class field theory.