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The database currently contains 39,293 postive definite integral lattices. It includes data from the Catalogue of Lattices.

The largest class number is 56, the largest dimension is 24, and the largest determinant is 191,102,976.

In the case of primitive integral lattices of class number one the database is complete.

Browse Integral Lattices

By Dimension: 1 2 3 4 5 6 7 8 9 10 ... 24

By Determinant: 1-4999 5000-9999 10000-19999 20000-24999 25000-29999 ... 1000000-191102976

By Class number: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... 56

Some of our favourite integral lattices: A2 Z2 D3 D3* 3.1942.3884.56.1 A5 E8 A14 Leech

A random integral lattice from the database.

Find a specific integral lattice by label or by name


e.g. 3.4.8.1.2, D3, E8, A14, Leech

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Dimension: e.g. 3 or 2-5
Determinant: e.g. 1 or 10-100
Level: e.g. 48 or 40-100
Gram matrix: e.g. $[5,1,23]$ for the Gram matrix $\begin{pmatrix}5 & 1\\ 1& 23\end{pmatrix}$
Minimal vector length: e.g. 1
Class number: e.g. 1
Automorphism group order: e.g. 696729600
Maximum number of integral lattices to display