Lattice Invariants
Dimension: | $3$ |
Determinant: | $236$ |
Level: | $472$ |
Density: | $0.272667017544141216723986108908\dots$ |
Group order: | $2$ |
Hermite number: | $0.647275730723863502764423509879\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $4$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 16 \end{array}\right)$
Genus Structure
Class number: | $7$ |
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 4 & 1 \\ 0 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 2 \\ -2 & 8 & 1 \\ 2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 2 \\ 1 & 2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 60 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 6 & -1 \\ 0 & -1 & 12 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.