The minimal models for rational projective smooth surfaces are $\mathbb{P}^2$ or the surfaces $\mathbb{F}_n$ for $n\neq 1$, where $$\mathbb{F_n}=\mathbb{P}_{\mathbb{P}^1}(\mathcal{O}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}(n)).$$ The right member of the equality is the projective bundle associated to the rank 2 vector bundle $\mathcal{O}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}(n)$ on $\mathbb{P}^1$.
The smooth quadric $\mathit{Q}\subset\mathbb{P}^3$ is a rational minimal surface since it does not contain exceptional curves.
My question is: am i right if i say that $\mathit{Q}\cong\mathbb{F}_0$ (birationally isomorphic)?