Properties

Label 3.758.1516.19.17
Class number 19
Dimension 3
Determinant 758
Level 1516

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Lattice Invariants

Dimension:$3$
Determinant:$758$
Level:$1516$
Label:$3.758.1516.19.17$
Density:$0.430327400421718609719845896129\dots$
Group order:$2$
Hermite number:$0.877405296630373430547647110620\dots$
Minimal vector length:$8$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & 1 \\ 1 & 1 & 12 \end{array}\right)$

Genus Structure

Class number:$19$
 
Genus representatives: $\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & 1 \\ 1 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & 5 \\ -4 & 10 & 0 \\ 5 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -1 \\ 2 & 10 & -2 \\ -1 & -2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 10 & -5 \\ 1 & -5 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -1 \\ 0 & -1 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & -3 \\ -4 & 10 & 2 \\ -3 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 10 & 4 \\ 1 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -1 \\ -1 & 10 & 2 \\ -1 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -3 \\ 2 & 10 & 2 \\ -3 & 2 & 16 \end{array}\right)$ ...
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Comments

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