Lattice Invariants
Dimension: | $9$ |
Determinant: | $16777216$ |
Level: | $8$ |
Density: | $0.000805300025082692106782740845641\dots$ |
Group order: | $11612160$ |
Hermite number: | $0.629960524947436582383605303639\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
$(0, 1, 0, 0, 0, 0, 0, 0, 0)$
|
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$\left(\begin{array}{rrrrrrrrr}
5 & -2 & 1 & -1 & 1 & 1 & 1 & 1 & -1 \\
-2 & 4 & -2 & 2 & -2 & -2 & -2 & -2 & 2 \\
1 & -2 & 13 & -5 & 5 & -3 & -3 & -3 & 3 \\
-1 & 2 & -5 & 13 & -5 & -5 & -5 & -5 & 5 \\
1 & -2 & 5 & -5 & 13 & 5 & -3 & 5 & -5 \\
1 & -2 & -3 & -5 & 5 & 13 & 5 & 5 & -5 \\
1 & -2 & -3 & -5 & -3 & 5 & 13 & 5 & -5 \\
1 & -2 & -3 & -5 & 5 & 5 & 5 & 13 & -5 \\
-1 & 2 & 3 & 5 & -5 & -5 & -5 & -5 & 13
\end{array}\right)$
Class number: | $1$ |
|
Genus representatives:
$\left(\begin{array}{rrrrrrrrr}
4 & -2 & 2 & 2 & -2 & -2 & -2 & -2 & 2 \\
-2 & 5 & -1 & -1 & 1 & 1 & 1 & 1 & -1 \\
2 & -1 & 13 & 5 & 3 & 3 & -5 & -5 & -3 \\
2 & -1 & 5 & 13 & -5 & -5 & -5 & -5 & -3 \\
-2 & 1 & 3 & -5 & 13 & 5 & 5 & -3 & -5 \\
-2 & 1 & 3 & -5 & 5 & 13 & -3 & 5 & 3 \\
-2 & 1 & -5 & -5 & 5 & -3 & 13 & -3 & -5 \\
-2 & 1 & -5 & -5 & -3 & 5 & -3 & 13 & 3 \\
2 & -1 & -3 & -3 & -5 & 3 & -5 & 3 & 13
\end{array}\right)$ |
| Download this matrix for
gp,
magma,
sage |