2 problems

Let $K=\mathbf{Q}(\beta)$ be the complex cubic field with $\beta$ the root of $x^3-x^2+5x+1$ having positive imaginary part, let $\mathfrak{f}=(3,\beta+1)$, and let $\mathfrak{a}$…

Let $K$ be a complex cubic number field and let $K(\mathfrak{f})$ be the narrow ray class field of conductor $\mathfrak{f}$. Let $I(\mathfrak{f})$ be the group of fractional ideals…