Properties

Label 3.236.472.7.4
Class number $7$
Dimension $3$
Determinant $236$
Level $472$

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Lattice Invariants

Dimension:$3$
Determinant:$236$
Level:$472$
Density:$0.272667017544141216723986108908\dots$
Group order:$2$
Hermite number:$0.647275730723863502764423509879\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 16 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$7$
 
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 4 & 1 \\ 0 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 2 \\ -2 & 8 & 1 \\ 2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 2 \\ 1 & 2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 60 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 6 & -1 \\ 0 & -1 & 12 \end{array}\right)$
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Comments

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