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
$\left(\begin{array}{rrr} 10 & 3 & 3 \\ 3 & 12 & -4 \\ 3 & -4 & 18 \end{array}\right)$
Genus Structure
Class number: | $40$ |
$\left(\begin{array}{rrr} 10 & 3 & 3 \\ 3 & 12 & -4 \\ 3 & -4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 3 & -5 \\ 3 & 12 & -4 \\ -5 & -4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 1 \\ -1 & 1 & 88 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -1 \\ 0 & 16 & -3 \\ -1 & -3 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & 3 \\ 0 & 14 & 1 \\ 3 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 24 & 8 \\ 0 & 8 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 14 & 2 \\ -1 & 2 & 60 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 70 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 4 & -1 \\ 4 & 14 & -6 \\ -1 & -6 & 16 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.