Lattice Invariants
| Dimension: | $3$ |
| Determinant: | $568$ |
| Level: | $1136$ |
| Density: | $0.497117938506256355113357881712\dots$ |
| Group order: | $2$ |
| Hermite number: | $0.965992768109033435879487126915\dots$ |
| Minimal vector length: | $8$ |
| Kissing number: | $4$ |
| Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 8 & 2 & 4 \\ 2 & 8 & 3 \\ 4 & 3 & 12 \end{array}\right)$
Genus Structure
| Class number: | $16$ |
| $\left(\begin{array}{rrr} 8 & 2 & 4 \\ 2 & 8 & 3 \\ 4 & 3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & -2 \\ 2 & 8 & -1 \\ -2 & -1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & 3 \\ 0 & 8 & -4 \\ 3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -4 & 4 \\ -4 & 10 & 1 \\ 4 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & 1 \\ -1 & 1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & -3 \\ 4 & 8 & 1 \\ -3 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 1 \\ 1 & 1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -1 \\ 0 & 8 & 0 \\ -1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 8 & -4 \\ -1 & -4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 3 \\ 2 & 6 & 3 \\ 3 & 3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & -1 \\ 4 & 8 & 0 \\ -1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & 0 \\ 0 & 8 & 3 \\ 0 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 8 & 1 \\ 0 & 1 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 36 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.