Simplest cubic fields with small class number

Akinari Hoshi, Hiroaki Iida

Let $m\in \mathbb{Z}$ be an integer and $L_m=\mathbb{Q}(\alpha )$ be the simplest cubic field with class number $h_m$ and conductor ${\mathfrak{f}}_m$ where $\alpha$ is a root of $f_m(X)=X^3-mX^…