Collection
Lattices from the Catalogue of Lattices
Records whose Gram tensor is from an entry of the catalogue of G. Nebe and N. J. A. Sloane.
The Gram tensor of each lattice is the section GRAM of
an entry of the Catalogue
of Lattices of G. Nebe and N. J. A. Sloane. The page of each lattice
links to its entry.
44 lattices
This collection in the database
| Tag | Lattice | Rank | Signature | Determinant | Properties |
|---|---|---|---|---|---|
| 0080 | \(K_{7}\) | 7 | (7, 0) | 384 | integral even not a root lattice |
| 0096 | \(K_{8}\) | 8 | (8, 0) | 576 | integral even not a root lattice |
| 0110 | \(\Lambda_{9}\) | 9 | (9, 0) | 512 | integral even not a root lattice |
| 0111 | \(K_{9}\) | 9 | (9, 0) | 864 | integral even not a root lattice |
| 0123 | \(\Lambda_{10}\) | 10 | (10, 0) | 768 | integral even not a root lattice |
| 0137 | \(\Lambda_{11}\) | 11 | (11, 0) | 1024 | integral even not a root lattice |
| 0149 | \(\Lambda_{12}\) | 12 | (12, 0) | 1024 | integral even not a root lattice |
| 0150 | \(K_{12}\) | 12 | (12, 0) | 729 | integral even 3-elementary not a root lattice |
| 0166 | \(\Lambda_{13}\) | 13 | (13, 0) | 1024 | integral even not a root lattice |
| 0178 | \(\Lambda_{14}\) | 14 | (14, 0) | 768 | integral even not a root lattice |
| 0193 | \(\Lambda_{15}\) | 15 | (15, 0) | 512 | integral even not a root lattice |
| 0205 | \(\Lambda_{16}\) | 16 | (16, 0) | 256 | integral even 2-elementary not a root lattice |
| 0219 | \(\Lambda_{17}\) | 17 | (17, 0) | 256 | integral even not a root lattice |
| 0231 | \(\Lambda_{18}\) | 18 | (18, 0) | 192 | integral even not a root lattice |
| 0245 | \(\Lambda_{19}\) | 19 | (19, 0) | 128 | integral even not a root lattice |
| 0257 | \(\Lambda_{20}\) | 20 | (20, 0) | 64 | integral even not a root lattice |
| 028S | \(\Lambda_{24}\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028T | \(N(A_{1}^{24})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028U | \(N(A_{2}^{12})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028V | \(N(A_{3}^{8})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028W | \(N(A_{4}^{6})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028X | \(N(D_{4}^{6})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028Y | \(N(A_{5}^{4} D_{4})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 028Z | \(N(A_{6}^{4})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0290 | \(N(D_{6}^{4})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0291 | \(N(E_{6}^{4})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0292 | \(N(A_{8}^{3})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0293 | \(N(D_{8}^{3})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0294 | \(E_{8}^{3}\) | 24 | (24, 0) | 1 | integral even unimodular root lattice |
| 0295 | \(N(A_{7}^{2} D_{5}^{2})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0296 | \(N(A_{9}^{2} D_{6})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0297 | \(N(A_{12}^{2})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0298 | \(N(D_{12}^{2})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 0299 | \(N(A_{11} D_{7} E_{6})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029A | \(N(A_{15} D_{9})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029B | \(N(A_{17} E_{7})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029C | \(N(A_{24})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029D | \(N(D_{10} E_{7}^{2})\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029E | \(D_{16}^{+} \oplus E_{8}\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 029F | \(D_{24}^{+}\) | 24 | (24, 0) | 1 | integral even unimodular not a root lattice |
| 02BQ | \(\mathrm{BGF.2.2112}\) | 2 | (2, 0) | 23 | integral even 23-elementary not a root lattice |
| 02BR | \(\mathrm{BGF.2.213}\) | 2 | (2, 0) | 5 | integral odd 5-elementary not a root lattice |
| 02BS | \(\mathrm{BGF.2.214}\) | 2 | (2, 0) | 7 | integral even 7-elementary not a root lattice |
| 02BT | \(\mathrm{BGF.2.216}\) | 2 | (2, 0) | 11 | integral even 11-elementary not a root lattice |