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The database currently contains 39,293 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.

Density and Hermite number of an integral lattice are computed in Magma using floating point approximation, digits displayed are guaranteed to be correct.

Browse Integral Lattices

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

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

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

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
Group order: e.g. 696729600
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