Properties

Label 3.172.344.5.1
Class number 5
Dimension 3
Determinant 172
Level 344

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Lattice Invariants

Dimension:$3$
Determinant:$172$
Level:$344$
Label:$3.172.344.5.1$
Density:$0.112922216037378813901920855687\dots$
Group order:$16$
Hermite number:$0.359628288929233526207296234225\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 44 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 8 & 0 \\ -1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 6 & 1 \\ 1 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -2 \\ 0 & 4 & 1 \\ -2 & 1 & 12 \end{array}\right)$
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Comments

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