Lattice Invariants
Dimension: | $3$ |
Determinant: | $334$ |
Level: | $668$ |
Density: | $0.229200402465098040950528896804\dots$ |
Group order: | $2$ |
Hermite number: | $0.576515740241033793947696982587\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 8 & 3 \\ 1 & 3 & 12 \end{array}\right)$
Genus Structure
Class number: | $13$ |
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 8 & 3 \\ 1 & 3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -1 \\ 2 & 8 & 1 \\ -1 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -2 \\ 0 & -2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & 1 \\ 0 & 1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 84 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 6 & 2 \\ -1 & 2 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 14 & -6 \\ -1 & -6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 2 & 0 \\ 1 & 0 & 112 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.