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Properties

Label 3.142.284.7.4
Class number $7$
Dimension $3$
Determinant $142$
Level $284$

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Lattice Invariants

Dimension:$3$
Determinant:$142$
Level:$284$
Density:$0.124279484626564088778339470428\dots$
Group order:$4$
Hermite number:$0.383354484072488162351587833289\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 12 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$7$
 
$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 8 & 1 \\ -1 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -2 \\ 0 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 48 \end{array}\right)$
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Comments

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