Properties

Label 3.194.388.5.1
Class number 5
Dimension 3
Determinant 194
Level 388

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Lattice Invariants

Dimension:$3$
Determinant:$194$
Level:$388$
Label:$3.194.388.5.1$
Density:$0.106326801774478221772975611087\dots$
Group order:$4$
Hermite number:$0.345485177209369974077917415769\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 28 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 4 & -2 \\ -1 & -2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & -1 \\ -2 & 6 & 0 \\ -1 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 6 & -3 \\ -1 & -3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 3 \\ -1 & 3 & 12 \end{array}\right)$
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Comments

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