Circles & Lines · Medium problem

A pentagon has vertices at the lattice points $A=(0,0)$, $B=(7,0)$, $C=(9,4)$, $D=(4,8)$, and $E=(-1,5)$. Its area is $56$ and it has exactly $12$ lattice points on its boundary (including the $5$ vertices). How many lattice points lie strictly inside it?