Integral lattices

The database currently contains 39,293 positive 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. Here are some further statistics.

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By dimension:	1  2  3  4  5  6  7  8  9  10  11  12  13  14  24
By determinant:	1-999  1000-9999  10000-99999  100000-999999  1000000-9999999  10000000-99999999  $\cdots$
By class number:	1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  50  51  52  54  55  56
Some interesting integral lattices or a random integral lattice

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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 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
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Label or name
e.g. 3.4.8.1.2, D3, E8, A14, Leech