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Properties

Label 3.362.724.10.10
Class number $10$
Dimension $3$
Determinant $362$
Level $724$

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Lattice Invariants

Dimension:$3$
Determinant:$362$
Level:$724$
Density:$0.404455934970637802343597537853\dots$
Group order:$2$
Hermite number:$0.841876512937986324272647377698\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 8 & 3 \\ 3 & 3 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$10$
 
$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 8 & 3 \\ 3 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 8 & -1 \\ 1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -1 \\ 2 & 6 & -2 \\ -1 & -2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 10 & -3 \\ 0 & -3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & 1 \\ -1 & 1 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 6 & 0 \\ -1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 14 & 6 \\ 1 & 6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 12 & 5 \\ 1 & 5 & 18 \end{array}\right)$
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Comments

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