Normal bundle of a curve in a quadric

Question

Let $C$ be a smooth curve on a smooth quadric $Q$ in $\mathbb P^3$. I have read in Hartshorne's Deformation Theory that the normal bundle of $C$ in $Q$ is $\mathcal N_{C/Q}\cong\mathcal O_C(C^2)$. Could you give me some hint on why is this true? Actually, I thought that the normal bundle should be $\mathcal O_C(C)$.

Answer 1

As John Brevik explained, $C^2$ here means a divisor, and not a number.