Lattice Invariants
| Dimension: | $3$ |
| Determinant: | $1658$ |
| Level: | $3316$ |
| Density: | $0.406636500515250534559368084868\dots$ |
| Group order: | $2$ |
| Hermite number: | $0.844899703934956449038864992205\dots$ |
| Minimal vector length: | $10$ |
| Kissing number: | $2$ |
| Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 14 \end{array}\right)$
Genus Structure
| Class number: | $40$ |
| $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 5 \\ 1 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 22 & -8 \\ 1 & -8 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & 4 \\ -1 & 12 & 5 \\ 4 & 5 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 8 & 2 \\ 0 & 2 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -2 \\ -3 & 16 & -1 \\ -2 & -1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 4 & 1 \\ 4 & 14 & 6 \\ 1 & 6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 20 & -9 \\ 1 & -9 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 10 & -1 \\ 1 & -1 & 22 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.