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Properties

Label 3.244.488.6.6
Class number $6$
Dimension $3$
Determinant $244$
Level $488$

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Lattice Invariants

Dimension:$3$
Determinant:$244$
Level:$488$
Density:$0.268159814257162939977736610828\dots$
Group order:$4$
Hermite number:$0.640122927207069444088144222544\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 6 q^{16} \) \(\mathstrut +\mathstrut 4 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 8 & 3 \\ 0 & 3 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$6$
 
$\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 8 & 3 \\ 0 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 8 & 1 \\ 0 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 6 & 2 \\ 2 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & -1 \\ -1 & -1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & -4 \\ 0 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 4 & -2 \\ 1 & -2 & 32 \end{array}\right)$
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Comments

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