Let \(\epsilon\) be a lattice equation. We say that \(\epsilon\) implies congruence modularity (congruence distributivity) if whenever \({\mathcal K}\) is a variety of algebras all of whose congruence lattices satisfy \(\epsilon\) then all of these lattices are modular (distributive). It is proved that the class of lattice equations which imply congruence modularity (congruence distributivity) is recursive. In other words, one can recursively decide if a lattice equation \(\epsilon\) implies congruence modularity (congruence distributivity).