Lattice Invariants
Dimension: | $3$ |
Determinant: | $412$ |
Level: | $824$ |
Density: | $0.583693685123204920936501247995\dots$ |
Group order: | $2$ |
Hermite number: | $1.07512158613286143022520345691\dots$ |
Minimal vector length: | $8$ |
Kissing number: | $6$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 8 & 3 & 2 \\ 3 & 8 & 1 \\ 2 & 1 & 8 \end{array}\right)$
Genus Structure
Class number: | $12$ |
$\left(\begin{array}{rrr} 8 & 3 & 2 \\ 3 & 8 & 1 \\ 2 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & 2 \\ -1 & 2 & 60 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 0 \\ 1 & 0 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -2 \\ 0 & 8 & 1 \\ -2 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 1 \\ 0 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 2 \\ -1 & 6 & 2 \\ 2 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 1 \\ 1 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & -1 \\ 1 & -1 & 104 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 0 \\ -2 & 8 & 3 \\ 0 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 4 & 0 \\ 1 & 0 & 52 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.