In some quadratic field, find a lattice M such that N(M)=1(norm of the lattice is 1) but M is not equal to the set of integers of the lattice.
I know that if we have an integral lattice, N(M)=1 implies M = O_m where O_m is set of integers of the lattice. So we should find a lattice which is not integral. But how? Can you find such a lattice?