Lattice Invariants
| Dimension: | $3$ |
| Determinant: | $1942$ |
| Level: | $3884$ |
| Density: | $0.268849349502595514816361808849\dots$ |
| Group order: | $2$ |
| Hermite number: | $0.641219781523573287039915855393\dots$ |
| Minimal vector length: | $8$ |
| Kissing number: | $2$ |
| Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 8 & 1 & 1 \\ 1 & 12 & -4 \\ 1 & -4 & 22 \end{array}\right)$
Genus Structure
| Class number: | $56$ |
| $\left(\begin{array}{rrr} 8 & 1 & 1 \\ 1 & 12 & -4 \\ 1 & -4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 5 & -3 \\ 5 & 12 & -4 \\ -3 & -4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 24 & -11 \\ -1 & -11 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 8 & 0 \\ 2 & 0 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -1 \\ 3 & 14 & -4 \\ -1 & -4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -3 \\ 1 & 12 & 5 \\ -3 & 5 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 22 & -9 \\ 1 & -9 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 18 & -2 \\ 3 & -2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 24 & -5 \\ 1 & -5 & 42 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.