Ideal class group of Q of square root minus thirty-one
= Ideal class group of Q of square root minus thirty-one
{title2=$\operatorname{Cl}(\mathbb Q(\sqrt{-31}))\cong C_3$}
The <ideal-form correspondence for imaginary quadratic fields> and the reduction bound $a\leq\sqrt{31/3}$ give exactly the forms $[1,1,8]$, $[2,1,4]$ and $[2,-1,4]$. Thus the <class number> is three and the ideal class group is cyclic of order three.