Lattice Invariants
Dimension: | $3$ |
Determinant: | $1886$ |
Level: | $3772$ |
Density: | $0.0964534497246906838846851659965\dots$ |
Group order: | $4$ |
Hermite number: | $0.323752225041188651959101294525\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 22 & -1 \\ 1 & -1 & 22 \end{array}\right)$
Genus Structure
Class number: | $27$ |
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 22 & -1 \\ 1 & -1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 22 & -8 \\ 2 & -8 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -2 & -2 \\ -2 & 16 & -7 \\ -2 & -7 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 5 & 4 \\ 5 & 14 & 2 \\ 4 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 18 & 8 \\ 1 & 8 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 2 \\ -1 & 10 & -3 \\ 2 & -3 & 50 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 4 \\ -3 & 16 & 0 \\ 4 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & -2 \\ -4 & 14 & 3 \\ -2 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 0 \\ 0 & 0 & 82 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.