Properties

Label 3.758.1516.19.18
Class number 19
Dimension 3
Determinant 758
Level 1516

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Lattice Invariants

Dimension:$3$
Determinant:$758$
Level:$1516$
Label:$3.758.1516.19.18$
Density:$0.601400824952334049570517504154\dots$
Group order:$2$
Hermite number:$1.09675662078796678818455888828\dots$
Minimal vector length:$10$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Class number:$19$
 
Genus representatives: $\left(\begin{array}{rrr} 10 & 4 & 3 \\ 4 & 10 & 2 \\ 3 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 4 & 5 \\ 4 & 10 & 0 \\ 5 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & 0 \\ -1 & 10 & 2 \\ 0 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 10 & -3 \\ 1 & -3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -2 \\ -3 & 10 & 3 \\ -2 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 10 & 4 \\ 1 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 10 & -2 \\ 1 & -2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 12 & -3 \\ -1 & -3 & 34 \end{array}\right)$ ...
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Comments

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