Let $X$ be a smooth divisor of degree $(1,1,2)$ in $\mathbb{P}^{1} \times \mathbb{P}^{1} \times \mathbb{P}^{2}$.
According to the list of Fano $3$-folds of Ivskovskikh-Prokhorov, this is a curve blow-up of $Y = \mathbb{P}^{1} \times \mathbb{P}^{2}$, in two different ways.
Question(s): How to describe (both) $ C \subset \mathbb{P}^{1} \times \mathbb{P}^{2}$ such that $Bl_{C}(Y)= X$?