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Properties

Label 3.310.620.8.8
Class number $8$
Dimension $3$
Determinant $310$
Level $620$

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Lattice Invariants

Dimension:$3$
Determinant:$310$
Level:$620$
Density:$0.437063612431196268088968253196\dots$
Group order:$2$
Hermite number:$0.886537993428974161327016677969\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 8 & 4 \\ 2 & 4 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$8$
 
$\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 8 & 4 \\ 2 & 4 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 6 & 2 \\ 2 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & -1 \\ 1 & -1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & 4 \\ 0 & 4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & 0 \\ 1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 78 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & 5 \\ 0 & 5 & 18 \end{array}\right)$
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Comments

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