Lattice Invariants
| Dimension: | $3$ |
| Determinant: | $1658$ |
| Level: | $3316$ |
| Density: | $0.102871801711073954965061860328\dots$ |
| Group order: | $2$ |
| Hermite number: | $0.337959881573982579615545996882\dots$ |
| Minimal vector length: | $4$ |
| Kissing number: | $2$ |
| Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 16 & 5 \\ 1 & 5 & 28 \end{array}\right)$
Genus Structure
| Class number: | $40$ |
| $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 16 & 5 \\ 1 & 5 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & 2 \\ -1 & 2 & 238 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 8 & 1 \\ 2 & 1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 22 & 8 \\ 1 & 8 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 2 \\ 0 & 16 & 1 \\ 2 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 16 & 7 \\ 2 & 7 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 12 & 5 \\ 2 & 5 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & -2 \\ -1 & 10 & -2 \\ -2 & -2 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & -1 \\ 1 & -1 & 14 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.