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Properties

Label 3.76.152.3.3
Class number $3$
Dimension $3$
Determinant $76$
Level $152$

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Lattice Invariants

Dimension:$3$
Determinant:$76$
Level:$152$
Density:$0.480487189430445296927065372248\dots$
Group order:$4$
Hermite number:$0.944326391417366842428700702634\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 8 q^{8} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 16 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 0 & 2 \\ 0 & 4 & 1 \\ 2 & 1 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$3$
 
$\left(\begin{array}{rrr} 4 & 0 & 2 \\ 0 & 4 & 1 \\ 2 & 1 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & -1 \\ -1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 20 \end{array}\right)$
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Comments

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