Lattice Invariants
Dimension: | $3$ |
Determinant: | $628$ |
Level: | $1256$ |
Density: | $0.0590967767028194282971722695383\dots$ |
Group order: | $4$ |
Hermite number: | $0.233548338010684891860710078226\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 4 \\ 1 & 4 & 28 \end{array}\right)$
Genus Structure
Class number: | $14$ |
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 4 \\ 1 & 4 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & 1 \\ 2 & 8 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 90 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -4 \\ 1 & 10 & -5 \\ -4 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 6 & -2 \\ 0 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 10 & 1 \\ -1 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & -4 \\ -1 & 8 & 1 \\ -4 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & -2 \\ 2 & 8 & 1 \\ -2 & 1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & 1 \\ 1 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 1 \\ 1 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 8 & -4 \\ -1 & -4 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 1 \\ 0 & 1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & -2 \\ -3 & 8 & 0 \\ -2 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 4 & -2 \\ 1 & -2 & 80 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.