  Let $C$ be a complex projective smooth curve and $W$ a symplectic vector
bundle of rank $2n$ over $C$. The Lagrangian Quot scheme $LQ_{-e}(W)$
parameterizes subsheaves of rank $n$ and degree $-e$ which are isotropic with
respect to the symplectic form. We prove that $LQ_{-e}(W)$ is irreducible and
generically smooth of the expected dimension for all large $e$, and that a
generic element is saturated and stable.
