Lattice Invariants
Dimension: | $3$ |
Determinant: | $358$ |
Level: | $716$ |
Density: | $0.0782712198808229144813069753372\dots$ |
Group order: | $4$ |
Hermite number: | $0.281666795872675122917344304257\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & 1 \\ 0 & 1 & 18 \end{array}\right)$
Genus Structure
Class number: | $13$ |
$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & 1 \\ 0 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 10 & 4 \\ -1 & 4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 90 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & -3 \\ -1 & -3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 3 \\ -1 & 3 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & -5 \\ 1 & -5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 8 & 1 \\ 1 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 120 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & 2 \\ -3 & 8 & 0 \\ 2 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 1 \\ -1 & 8 & 4 \\ 1 & 4 & 10 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.