Lattice Invariants
Dimension: | $3$ |
Determinant: | $758$ |
Level: | $1516$ |
Density: | $0.601400824952334049570517504154\dots$ |
Group order: | $2$ |
Hermite number: | $1.09675662078796678818455888828\dots$ |
Minimal vector length: | $10$ |
Kissing number: | $4$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 10 & 4 & 5 \\ 4 & 10 & 4 \\ 5 & 4 & 12 \end{array}\right)$
Genus Structure
Class number: | $19$ |
$\left(\begin{array}{rrr} 10 & 4 & 5 \\ 4 & 10 & 4 \\ 5 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 4 & -3 \\ 4 & 10 & -2 \\ -3 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & 1 \\ 2 & 10 & -4 \\ 1 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 10 & -2 \\ -1 & -2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 0 \\ 1 & 10 & -2 \\ 0 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & -2 \\ 1 & -2 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -2 \\ -3 & 10 & 3 \\ -2 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 6 & 1 \\ -1 & 1 & 32 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.