Lattice Database

A catalogue of 434 lattices of rank 1 to 28. Each lattice has a permanent tag.

By rank

Degenerate lattices 7
Lattices on which the correlation has a nonzero kernel.
Even unimodular lattices 41
Integral lattices with determinant \(1\) or \(-1\) on which every value \(b(x, x)\) is even.
Hyperbolic lattices 124
Nondegenerate lattices of rank at least 2 with signature \((1, n)\) or \((n, 1)\).
Lattices from the Catalogue of Lattices 44
Records whose Gram tensor is from an entry of the catalogue of G. Nebe and N. J. A. Sloane.
Nikulin's 2-elementary lattices 75
The invariant lattices of the nonsymplectic involutions of K3 surfaces, by Nikulin's invariants \((r, a, \delta)\).
Lattices that are not integral 39
Lattices whose form has a value outside the integers.
Even hyperbolic 2-elementary lattices with \(r + a = 22\) 12
The rows of Nikulin's Table 1 with \(r + a = 22\), with the reflectivity of each from Alexeev's Theorem 1.1.
Root lattices 292
Lattices \(L\) with \(L = \mathbb{Z}\Phi(L)\).
2-elementary lattices 106
Integral lattices with discriminant group \((\mathbb{Z}/2)^a\), \(a \geq 1\).