Properties

Label 3.212.424.5.3
Class number 5
Dimension 3
Determinant 212
Level 424

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Lattice Invariants

Dimension:$3$
Determinant:$212$
Level:$424$
Label:$3.212.424.5.3$
Density:$0.287687292396101625716656865242\dots$
Group order:$4$
Hermite number:$0.670833441507507800355129528843\dots$
Minimal vector length:$4$
Kissing Number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 4 & 1 \\ 1 & 1 & 18 \end{array}\right)$

Genus Structure

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

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