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Properties

Label 3.82.164.4.4
Class number $4$
Dimension $3$
Determinant $82$
Level $164$

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Lattice Invariants

Dimension:$3$
Determinant:$82$
Level:$164$
Density:$0.163544781010908816216310965145\dots$
Group order:$4$
Hermite number:$0.460354131224054770194086521256\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 1 \\ 1 & 1 & 8 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$4$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 1 \\ 1 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 6 & 2 \\ 1 & 2 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 2 & 0 \\ 1 & 0 & 28 \end{array}\right)$
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Comments

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