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Properties

Name A1+A2
Label 3.6.12.1.2
Class number $1$
Dimension $3$
Determinant $6$
Level $12$

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Lattice Invariants

Dimension:$3$
Determinant:$6$
Level:$12$
Density:$0.604599788078072616864692752547\dots$
Group order:$24$
Hermite number:$1.10064241629820889462486998414\dots$
Minimal vector length:$2$
Kissing number:$8$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 8 q^{2} \) \(\mathstrut +\mathstrut 12 q^{4} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 20 q^{8} \) \(\mathstrut +\mathstrut 24 q^{10} \) \(\mathstrut +\mathstrut 24 q^{14} \) \(\mathstrut +\mathstrut 36 q^{16} \) \(\mathstrut +\mathstrut 8 q^{18} \) \(\mathstrut +\mathstrut 24 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 2 \end{array}\right)$
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Comments

This integral lattice is the A1+A2 lattice.

This is the hexagonal P Bravais lattice of even holotype..