Lattice Invariants
Dimension: | $8$ |
Determinant: | $4096$ |
Level: | $4$ |
Density: | $0.00396358606095387521307130259962\dots$ |
Group order: | $622080$ |
Hermite number: | $0.707106781186547524400844362105\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $6$ |
Normalized minimal vectors: |
$(1, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, 0, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0, 0)$
|
| Download this list for
gp,
magma,
sage |
$\left(\begin{array}{rrrrrrrr}
2 & -1 & 1 & -1 & 1 & 1 & 1 & 1 \\
-1 & 2 & -1 & 1 & 0 & 0 & 0 & 0 \\
1 & -1 & 6 & -2 & 3 & 3 & 3 & 3 \\
-1 & 1 & -2 & 6 & -3 & -3 & -3 & -3 \\
1 & 0 & 3 & -3 & 6 & 2 & 2 & 2 \\
1 & 0 & 3 & -3 & 2 & 6 & 2 & 2 \\
1 & 0 & 3 & -3 & 2 & 2 & 6 & 2 \\
1 & 0 & 3 & -3 & 2 & 2 & 2 & 6
\end{array}\right)$
Class number: | $1$ |
|
Genus representatives:
$\left(\begin{array}{rrrrrrrr}
2 & -1 & 1 & -1 & -1 & -1 & -1 & -1 \\
-1 & 2 & -1 & 1 & 1 & 1 & 1 & 1 \\
1 & -1 & 6 & 2 & -2 & 2 & 2 & 2 \\
-1 & 1 & 2 & 6 & -2 & 2 & 2 & 2 \\
-1 & 1 & -2 & -2 & 6 & -2 & -2 & -2 \\
-1 & 1 & 2 & 2 & -2 & 6 & 2 & 2 \\
-1 & 1 & 2 & 2 & -2 & 2 & 6 & 2 \\
-1 & 1 & 2 & 2 & -2 & 2 & 2 & 6
\end{array}\right)$ |
| Download this matrix for
gp,
magma,
sage |