Let $\mathcal{O}_l=\mathbb{Z}[\frac{1+\sqrt{-l}}{2}]$ with $l$ a prime number congruent to 3 mod 4. Let $\mathfrak{a}$ be a non-principal fractional ideal of $\mathcal{O}_l$.
My questions are: Why N$(x)$/N$(\mathfrak{a})$ is less than $\frac{1+l}{4}$, being $x$ a generator of $\mathfrak{a}$? Why the fundamental parallelogram of $\mathfrak{a}$ have area equal to $\frac{\sqrt{-l}}{2}$?
I've been told that it is crucial that the discriminant is prime, so I thought about Minkowsky's theorems but I do not get to do it.
I would be thankful if you could help me.