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Properties

Label 3.22.44.2.1
Class number $2$
Dimension $3$
Determinant $22$
Level $44$

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Lattice Invariants

Dimension:$3$
Determinant:$22$
Level:$44$
Density:$0.315741941699827645476544793939\dots$
Group order:$8$
Hermite number:$0.713765855503608170671899991762\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 12 q^{8} \) \(\mathstrut +\mathstrut 12 q^{10} \) \(\mathstrut +\mathstrut 8 q^{12} \) \(\mathstrut +\mathstrut 8 q^{14} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 16 q^{18} \) \(\mathstrut +\mathstrut 16 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$2$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 8 \end{array}\right)$
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Comments

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