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Properties

Label 3.12.24.1.4
Class number $1$
Dimension $3$
Determinant $12$
Level $24$

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Lattice Invariants

Dimension:$3$
Determinant:$12$
Level:$24$
Density:$0.427516610053954698514678786556\dots$
Group order:$8$
Hermite number:$0.873580464736298869047220426814\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 8 q^{3} \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 8 q^{7} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 8 q^{11} \) \(\mathstrut +\mathstrut 12 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 24 q^{15} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 14 q^{18} \) \(\mathstrut +\mathstrut 8 q^{19} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 3 & -1 \\ -1 & -1 & 3 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 3 & -1 \\ -1 & -1 & 3 \end{array}\right)$
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Comments

This is the digonal I Bravais lattice of classical holotype. Also called the orthorhombic I Bravais lattice..