Lattice Invariants
| Dimension: | $3$ |
| Determinant: | $652$ |
| Level: | $1304$ |
| Density: | $0.301371167131367980298371544877\dots$ |
| Group order: | $2$ |
| Hermite number: | $0.691940448085541096344503671085\dots$ |
| Minimal vector length: | $6$ |
| Kissing number: | $2$ |
| Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 10 & -1 \\ 1 & -1 & 12 \end{array}\right)$
Genus Structure
| Class number: | $14$ |
| $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 10 & -1 \\ 1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & -3 \\ -3 & 10 & 5 \\ -3 & 5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & -2 \\ 3 & 8 & 1 \\ -2 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 12 & -5 \\ 0 & -5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & -3 \\ -2 & 8 & 1 \\ -3 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 1 \\ -3 & 8 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 8 & 1 \\ -1 & 1 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 4 & -2 \\ -1 & -2 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 20 & -8 \\ 0 & -8 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & -2 \\ 1 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 18 & -5 \\ -1 & -5 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 8 & 2 \\ 0 & 2 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 164 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.