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

Counting maximal Lagrangian subbundles over an algebraic curve