We study the local symplectic algebra of curves. We use the method of
algebraic restrictions to classify symplectic $T_7$ singularities. We define
discrete symplectic invariants - the Lagrangian tangency orders. We use these
invariants to distinguish symplectic singularities of classical $A-D-E$
singularities of planar curves, $S_5$ singularity and $T_7$ singularity. We
also give the geometric description of these symplectic singularities.