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Properties

Label 3.478.956.18.1
Class number $18$
Dimension $3$
Determinant $478$
Level $956$

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Lattice Invariants

Dimension:$3$
Determinant:$478$
Level:$956$
Density:$0.0677375785284977345442291329124\dots$
Group order:$8$
Hermite number:$0.255792239034937553691457808086\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 8 q^{10} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 120 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$18$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 120 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 16 & -7 \\ 0 & -7 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 14 & 2 \\ 0 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 16 & 3 \\ 0 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 2 & 0 \\ 1 & 0 & 160 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 8 & -3 \\ -2 & -3 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 1 \\ 0 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & -4 \\ 1 & -4 & 26 \end{array}\right)$ ...
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Comments

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