New invariants for integral lattices

Let $\mathrm{\Lambda }$ be any integral lattice in Euclidean space. It has been shown that for every integer $n>0$, there is a hypersphere that passes through exactly $n$ points of $\mathrm{\Lambda }$. Using this result, we introduce new lattice invariants and give some computational results related to two-dimensional Euclidean lattices of class number one.