Database
Every lattice of the catalogue, with its invariants. The minimum, the kissing number, the order of the isometry group and the types of \(\Phi_{\{2\}}(L)\) and \(\Phi(L)\) are columns of the definite lattices. An empty cell in Integral overlattices is not decided. Each column is defined on the fields page; \(R(L) = \mathbb{Z}\Phi(L)\) is the root sublattice.
| Tag | Lattice | Rank | Signature | Determinant | Definiteness | Properties | Discriminant group | Minimum | Kissing number | Isometry group order | Type of Φ{2}(L) | Genus symbol | Families | Other names | n₊ | n₋ | Type of Φ(L) | R(L) = ℤΦ(L) | [L : R(L)], when finite | Rank of R(L) | R(L) primitive in L | Integral overlattices | Nikulin δ |
|---|