Properties

Label 2.4.8.1.1
Class number 1
Dimension 2
Determinant 4
Level 8

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Lattice Invariants

Dimension:$2$
Determinant:$4$
Level:$8$
Label:$2.4.8.1.1$
Density:$0.392699081698724154807830422910\dots$
Group order:$4$
Hermite number:$0.500000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$2$
Normalized minimal vectors: $(1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rr} 1 & 0 \\ 0 & 4 \end{array}\right)$

Genus Structure

Class number:$1$
 
Genus representatives: $\left(\begin{array}{rr} 1 & 0 \\ 0 & 4 \end{array}\right)$
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