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Properties

Label 3.138.276.5.4
Class number $5$
Dimension $3$
Determinant $138$
Level $276$

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Lattice Invariants

Dimension:$3$
Determinant:$138$
Level:$276$
Density:$0.356573501780269125612525425609\dots$
Group order:$4$
Hermite number:$0.774046341897226496947774742279\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 6 \end{array}\right)$

Genus Structure

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

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