Collection
Even unimodular lattices
Integral lattices with determinant \(1\) or \(-1\) on which every value \(b(x, x)\) is even.
Each member is even and unimodular.
41 lattices
This collection in the database
| Tag | Lattice | Rank | Signature | Determinant | Properties |
|---|---|---|---|---|---|
| 0016 | \(U\) | 2 | (1, 1) | -1 | integral even unimodular not a root lattice hyperbolic isotropic |
| 0040 | \(U^{2}\) | 4 | (2, 2) | 1 | integral even unimodular root lattice isotropic |
| 0067 | \(U^{3}\) | 6 | (3, 3) | -1 | integral even unimodular root lattice isotropic |
| 0094 | \(E_{8}\) | 8 | (8, 0) | 1 | integral even unimodular root lattice |
| 0099 | \(U^{4}\) | 8 | (4, 4) | 1 | integral even unimodular root lattice isotropic |
| 0128 | \(U \oplus E_{8}(-1)\) | 10 | (1, 9) | -1 | integral even unimodular root lattice hyperbolic isotropic |
| 0156 | \(U^{2} \oplus E_{8}(-1)\) | 12 | (2, 10) | 1 | integral even unimodular root lattice isotropic |
| 0183 | \(U^{3} \oplus E_{8}(-1)\) | 14 | (3, 11) | -1 | integral even unimodular root lattice isotropic |
| 0206 | \(D_{16}^{+}\) | 16 | (16, 0) | 1 | integral even unimodular not a root lattice |
| 0210 | \(U^{4} \oplus E_{8}(-1)\) | 16 | (4, 12) | 1 | integral even unimodular root lattice isotropic |
| 0213 | \(E_{8}^{2}\) | 16 | (16, 0) | 1 | integral even unimodular root lattice |
| 0236 | \(U \oplus E_{8}(-1)^{2}\) | 18 | (1, 17) | -1 | integral even unimodular root lattice hyperbolic isotropic |
| 0261 | \(U^{2} \oplus E_{8}(-1)^{2}\) | 20 | (2, 18) | 1 | integral even unimodular root lattice isotropic |
| 027E | \(U^{3} \oplus E_{8}(-1)^{2}\) | 22 | (3, 19) | -1 | integral even unimodular root lattice isotropic |
| 027F | \(U^{4} \oplus E_{8}(-1)^{2}\) | 24 | (4, 20) | 1 | integral even unimodular root lattice isotropic |
| 027G | \(U \oplus E_{8}(-1)^{3}\) | 26 | (1, 25) | -1 | integral even unimodular root lattice hyperbolic isotropic |
| 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 |
| 029K | \(U^{2} \oplus E_{8}(-1)^{3}\) | 28 | (2, 26) | 1 | integral even unimodular root lattice isotropic |