Lattice Invariants
Dimension: | $3$ |
Determinant: | $568$ |
Level: | $1136$ |
Density: | $0.175757732683625500194296343173\dots$ |
Group order: | $4$ |
Hermite number: | $0.482996384054516717939743563457\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 4 \\ 1 & 4 & 20 \end{array}\right)$
Genus Structure
Class number: | $16$ |
$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 4 \\ 1 & 4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & -1 \\ 1 & -1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & -3 \\ 0 & 8 & 4 \\ -3 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & -3 \\ 0 & 8 & 0 \\ -3 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 8 & -2 \\ 1 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & -3 \\ -2 & 6 & 3 \\ -3 & 3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & -3 \\ 2 & 8 & -4 \\ -3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -4 & 3 \\ -4 & 8 & -4 \\ 3 & -4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 8 & -4 \\ 1 & -4 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 0 \\ 4 & 10 & -5 \\ 0 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 6 & 1 \\ 1 & 1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -4 & 1 \\ -4 & 8 & 0 \\ 1 & 0 & 12 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.