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Properties

Label 5.1.2.1.1
Class number $1$
Dimension $5$
Determinant $1$
Level $2$

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Lattice Invariants

Dimension:$5$
Determinant:$1$
Level:$2$
Density:$0.164493406684822643647241516665\dots$
Group order:$3840$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$10$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$, $(0, 0, 0, 0, 1)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 10 q \) \(\mathstrut +\mathstrut 40 q^{2} \) \(\mathstrut +\mathstrut 80 q^{3} \) \(\mathstrut +\mathstrut 90 q^{4} \) \(\mathstrut +\mathstrut 112 q^{5} \) \(\mathstrut +\mathstrut 240 q^{6} \) \(\mathstrut +\mathstrut 320 q^{7} \) \(\mathstrut +\mathstrut 200 q^{8} \) \(\mathstrut +\mathstrut 250 q^{9} \) \(\mathstrut +\mathstrut 560 q^{10} \) \(\mathstrut +\mathstrut 560 q^{11} \) \(\mathstrut +\mathstrut 400 q^{12} \) \(\mathstrut +\mathstrut 560 q^{13} \) \(\mathstrut +\mathstrut 800 q^{14} \) \(\mathstrut +\mathstrut 960 q^{15} \) \(\mathstrut +\mathstrut 730 q^{16} \) \(\mathstrut +\mathstrut 480 q^{17} \) \(\mathstrut +\mathstrut 1240 q^{18} \) \(\mathstrut +\mathstrut 1520 q^{19} \) \(\mathstrut +\mathstrut 752 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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