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Properties

Name I2+A1
Label 3.2.4.1.1
Class number $1$
Dimension $3$
Determinant $2$
Level $4$

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Lattice Invariants

Dimension:$3$
Determinant:$2$
Level:$4$
Density:$0.370240244846530520584656749172\dots$
Group order:$16$
Hermite number:$0.793700525984099737375852819636\dots$
Minimal vector length:$1$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 8 q^{3} \) \(\mathstrut +\mathstrut 12 q^{4} \) \(\mathstrut +\mathstrut 8 q^{5} \) \(\mathstrut +\mathstrut 8 q^{6} \) \(\mathstrut +\mathstrut 16 q^{7} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{9} \) \(\mathstrut +\mathstrut 24 q^{10} \) \(\mathstrut +\mathstrut 8 q^{11} \) \(\mathstrut +\mathstrut 24 q^{12} \) \(\mathstrut +\mathstrut 24 q^{13} \) \(\mathstrut +\mathstrut 16 q^{15} \) \(\mathstrut +\mathstrut 12 q^{16} \) \(\mathstrut +\mathstrut 16 q^{17} \) \(\mathstrut +\mathstrut 30 q^{18} \) \(\mathstrut +\mathstrut 24 q^{19} \) \(\mathstrut +\mathstrut 24 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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

This integral lattice is the I2+A1 lattice.

This is the tetragonal P Bravais lattice of classical holotype..