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Properties

Label 3.706.1412.19.1
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:$12$
Hermite number:$0.224609659072293705004237941435\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 236 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$19$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 236 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 14 & -5 \\ 0 & -5 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 14 & 4 \\ 0 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & 1 \\ -1 & 1 & 102 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & -1 \\ -2 & 6 & -1 \\ -1 & -1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 16 & -6 \\ -1 & -6 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 12 & -6 \\ -2 & -6 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 3 \\ 1 & 8 & 4 \\ 3 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & 5 \\ -1 & 5 & 32 \end{array}\right)$ ...
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Comments

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