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Properties

Label 5.12.24.1.2
Class number $1$
Dimension $5$
Determinant $12$
Level $24$

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Lattice Invariants

Dimension:$5$
Determinant:$12$
Level:$24$
Density:$0.0474851563147004697631749245873\dots$
Group order:$64$
Hermite number:$0.608364341893205759287997108339\dots$
Minimal vector length:$1$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 16 q^{3} \) \(\mathstrut +\mathstrut 46 q^{4} \) \(\mathstrut +\mathstrut 48 q^{5} \) \(\mathstrut +\mathstrut 22 q^{6} \) \(\mathstrut +\mathstrut 80 q^{7} \) \(\mathstrut +\mathstrut 138 q^{8} \) \(\mathstrut +\mathstrut 76 q^{9} \) \(\mathstrut +\mathstrut 68 q^{10} \) \(\mathstrut +\mathstrut 144 q^{11} \) \(\mathstrut +\mathstrut 204 q^{12} \) \(\mathstrut +\mathstrut 208 q^{13} \) \(\mathstrut +\mathstrut 108 q^{14} \) \(\mathstrut +\mathstrut 176 q^{15} \) \(\mathstrut +\mathstrut 398 q^{16} \) \(\mathstrut +\mathstrut 312 q^{17} \) \(\mathstrut +\mathstrut 114 q^{18} \) \(\mathstrut +\mathstrut 336 q^{19} \) \(\mathstrut +\mathstrut 552 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 2 & 1 & 1 \\ 0 & 0 & 1 & 3 & 1 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 2 & 1 & 1 \\ 0 & 0 & 1 & 3 & 1 \\ 0 & 0 & 1 & 1 & 3 \end{array}\right)$
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