Properties

Label 3.706.1412.19.15
Class number 19
Dimension 3
Determinant 706
Level 1412

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Lattice Invariants

Dimension:$3$
Determinant:$706$
Level:$1412$
Label:$3.706.1412.19.15$
Density:$0.289616397670481146418560497894\dots$
Group order:$2$
Hermite number:$0.673828977216881115012713824306\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 10 & 4 \\ 2 & 4 & 14 \end{array}\right)$

Genus Structure

Class number:$19$
 
Genus representatives: $\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 10 & 4 \\ 2 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & -1 \\ -1 & -1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & -2 \\ 1 & 12 & 6 \\ -2 & 6 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 14 & -2 \\ 1 & -2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 5 \\ 1 & 5 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 14 & -2 \\ 1 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 3 \\ -3 & 10 & -4 \\ 3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 14 & 4 \\ -1 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 10 & 1 \\ 1 & 1 & 18 \end{array}\right)$ ...
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Comments

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