Properties

Label 3.472.944.12.3
Class number $12$
Dimension $3$
Determinant $472$
Level $944$

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Lattice Invariants

Dimension:$3$
Determinant:$472$
Level:$944$
Density:$0.0681667543860353041809965272271\dots$
Group order:$8$
Hermite number:$0.256871543966136484393789596141\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 4 \\ 1 & 4 & 32 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$12$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 4 \\ 1 & 4 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & 0 \\ -1 & 0 & 68 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & -4 \\ 4 & 8 & -3 \\ -4 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 8 & -1 \\ -1 & -1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & 0 \\ 2 & 8 & 1 \\ 0 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 0 \\ 4 & 8 & 1 \\ 0 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & 3 \\ 2 & 8 & -2 \\ 3 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 8 & 3 \\ 1 & 3 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & 1 \\ -1 & 1 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & -1 \\ 1 & -1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & -4 \\ 1 & -4 & 12 \end{array}\right)$
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.