Properties

Label 3.158.316.6.5
Class number $6$
Dimension $3$
Determinant $158$
Level $316$

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Lattice Invariants

Dimension:$3$
Determinant:$158$
Level:$316$
Density:$0.117818929473065261110928862016\dots$
Group order:$4$
Hermite number:$0.369951080438653685102336802406\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & 4 \\ 0 & 4 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$6$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & 4 \\ 0 & 4 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -1 \\ 0 & -1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & -2 \\ 1 & -2 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 6 & -2 \\ -1 & -2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 20 \end{array}\right)$
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Comments

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