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Properties

Label 3.270.540.6.3
Class number $6$
Dimension $3$
Determinant $270$
Level $540$

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Lattice Invariants

Dimension:$3$
Determinant:$270$
Level:$540$
Density:$0.0901284150216358199322880171178\dots$
Group order:$8$
Hermite number:$0.309439255574185259494005090061\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & 5 \\ 0 & 5 & 16 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$6$
 
$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & 0 \\ 1 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 1 \\ -1 & 6 & -1 \\ 1 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & 1 \\ 0 & 1 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & 4 \\ 1 & 4 & 14 \end{array}\right)$
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Comments

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