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Properties

Label 3.502.1004.18.18
Class number $18$
Dimension $3$
Determinant $502$
Level $1004$

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Lattice Invariants

Dimension:$3$
Determinant:$502$
Level:$1004$
Density:$0.528788186602414149365559444143\dots$
Group order:$2$
Hermite number:$1.00659649679228794604021065478\dots$
Minimal vector length:$8$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 8 & 1 \\ 4 & 1 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$18$
 
$\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 8 & 1 \\ 4 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & 1 \\ 0 & 1 & 72 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 6 & 1 \\ 0 & 1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 14 & -4 \\ 1 & -4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 8 & 0 \\ -1 & 0 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 1 \\ -1 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 10 & -2 \\ -1 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 5 \\ 0 & 5 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 8 & -3 \\ -2 & -3 & 18 \end{array}\right)$ ...
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Comments

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