Properties

Label 3.670.1340.13.7
Class number 13
Dimension 3
Determinant 670
Level 1340

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Lattice Invariants

Dimension:$3$
Determinant:$670$
Level:$1340$
Label:$3.670.1340.13.7$
Density:$0.0572145141598155511413952076378\dots$
Group order:$4$
Hermite number:$0.228562544075420422091375082215\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 18 & 5 \\ 0 & 5 & 20 \end{array}\right)$

Genus Structure

Class number:$13$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 18 & 5 \\ 0 & 5 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 168 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -1 \\ 0 & -1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 14 & 5 \\ 0 & 5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 18 & -4 \\ 1 & -4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 1 \\ 0 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 8 & 2 \\ 2 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 3 \\ -2 & 10 & 0 \\ 3 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 10 & -1 \\ -1 & -1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 18 & 3 \\ 1 & 3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 1 \\ -1 & 10 & 2 \\ 1 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 5 \\ 0 & 5 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 8 & 3 \\ -1 & 3 & 46 \end{array}\right)$
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Comments

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