  Let $C$ be a smooth projective curve and $W$ a symplectic bundle over $C$.
Let $LQ_e (W)$ be the Lagrangian Quot scheme parametrizing Lagrangian
subsheaves $E \subset W$ of degree $e$. We give a closed formula for
intersection numbers on $LQ_e (W)$. As a special case, for $g \ge 2$, we
compute the number of Lagrangian subbundles of maximal degree of a general
stable symplectic bundle, when this is finite. This is a symplectic analogue of
Holla's enumeration of maximal subbundles in [13].
