Properties

Label 3.222.444.5.4
Class number 5
Dimension 3
Determinant 222
Level 444

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Lattice Invariants

Dimension:$3$
Determinant:$222$
Level:$444$
Label:$3.222.444.5.4$
Density:$0.0993955928850687672771220803619\dots$
Group order:$8$
Hermite number:$0.330302862564371523213012705188\dots$
Minimal vector length:$2$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 3 \\ 0 & 3 & 20 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 3 \\ 0 & 3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & -1 \\ 0 & -1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 2 & 0 \\ 0 & 0 & 74 \end{array}\right)$
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Comments

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