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Properties

Label 3.706.1412.19.4
Class number $19$
Dimension $3$
Determinant $706$
Level $1412$

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Lattice Invariants

Dimension:$3$
Determinant:$706$
Level:$1412$
Density:$0.0557367017189273313556116444587\dots$
Group order:$4$
Hermite number:$0.224609659072293705004237941435\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut 4 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 30 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$19$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & 5 \\ 1 & 5 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 10 & 4 \\ -2 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 14 & -2 \\ 1 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & 1 \\ -1 & 1 & 102 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & -3 \\ 1 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & -2 \\ 1 & 12 & 6 \\ -2 & 6 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 14 & -1 \\ 1 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 16 & 7 \\ 1 & 7 & 26 \end{array}\right)$ ...
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Comments

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