Two Integer symmetric matrixes $A$ and $B$ are called equivalent with each other, if there exists $γ \in SL(2,Z)$ such that $B = γ^{T}Aγ$.
Obviously, equivalent matrixes share the same determinant. How can I find out all equivalence classes of $det = 56$? In other words, how can I divide all integer symmetric matrixes $A: |A| = 56$ into different equivalence classes?