(a) Write down $\mathcal{O}_{K}$, when $K=\mathbb{Q}(\sqrt{\delta})$, and $\delta \equiv 2$ or $3(\bmod 4)$. [You need not prove your answer.]

Let $L=\mathbb{Q}(\sqrt{2}, \sqrt{\delta})$, where $\delta \equiv 3(\bmod 4)$ is a square-free integer. Find an integral basis of $\mathcal{O}_{L} \cdot$ [Hint: Begin by considering the relative traces $t r_{L / K}$, for $K$ a quadratic subfield of $L .]$

(b) Compute the ideal class group of $\mathbb{Q}(\sqrt{-14})$.