Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 123 / 2 / 2 / 6 / Solution

For $K=\mathbb{Q}(\sqrt{-11})$, the fundamental discriminant is $-11$ and ${\chi }_{-11}(2)=-1$ because $-11\equiv 5(\mathrm{mod}8)$. The quadratic residues modulo $11$ areThereforeThe quadratic class number formula gives