Lattice Invariants
Dimension: | $3$ |
Determinant: | $298$ |
Level: | $596$ |
Density: | $0.445776700979343866315264613974\dots$ |
Group order: | $2$ |
Hermite number: | $0.898281583068429893553931891015\dots$ |
Minimal vector length: | $6$ |
Kissing number: | $4$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 6 & 2 & 2 \\ 2 & 6 & 1 \\ 2 & 1 & 10 \end{array}\right)$
Genus Structure
Class number: | $10$ |
$\left(\begin{array}{rrr} 6 & 2 & 2 \\ 2 & 6 & 1 \\ 2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 2 \\ 0 & 8 & -3 \\ 2 & -3 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 6 & 2 \\ 1 & 2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 6 & 1 \\ 2 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 4 & 1 \\ 1 & 1 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & 2 \\ 1 & 2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 6 & -2 \\ -1 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 0 \\ -1 & 0 & 100 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.