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Properties

Label 3.478.956.18.7
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:$4$
Hermite number:$0.255792239034937553691457808086\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 1 \\ 0 & 1 & 32 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$18$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 1 \\ 0 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 4 \\ 1 & 4 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & 1 \\ -2 & 8 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 16 & -3 \\ 0 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 8 & 4 \\ -2 & 4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 6 & 0 \\ -1 & 0 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 5 \\ 0 & 5 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 0 \\ -3 & 8 & -3 \\ 0 & -3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 16 & 9 \\ 0 & 9 & 20 \end{array}\right)$ ...
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Comments

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