I'm working through a final exam from 2 years ago. First task was to find the ideal class group of $\Bbb{Q}(\sqrt{-73})$. That is not the difficult work. I can give the 4 representants of the group by $\omega$, $\frac{\omega+1}{2}$, $\frac{\omega+2}{7}$ and $\frac{\omega-2}{7}$ with $\omega=\sqrt{-73}$. This group is isomorphic to $C_4$. A generator for the group is given by $C=\frac{\omega-2}{7}$ (I hope this is true :) ) But now the following task:
Compute all ideals $\mathfrak{a}$ from $\Bbb{Z}[\sqrt{-73}]$ such that $N(\mathfrak{a})<15$ with $\mathfrak{a}\in C$ (here is N the Norm of the ideal).
Can someone help me with this question?! Thanks :)