Properties

Label 3.138.276.5.5
Class number 5
Dimension 3
Determinant 138
Level 276

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Lattice Invariants

Dimension:$3$
Determinant:$138$
Level:$276$
Label:$3.138.276.5.5$
Density:$0.655067351369286388634255668374\dots$
Group order:$4$
Hermite number:$1.16106951284583974542166211342\dots$
Minimal vector length:$6$
Kissing Number:$8$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 6 & 2 \\ 2 & 2 & 6 \end{array}\right)$

Genus Structure

Class number:$5$
 
Genus representatives: $\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 6 & 2 \\ 2 & 2 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & 0 \\ -1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & 1 \\ -1 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 6 & 0 \\ 0 & 0 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 2 & 0 \\ 0 & 0 & 46 \end{array}\right)$
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Comments

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