Properties

Label 2.19.19.1.1
Class number 1
Dimension 2
Determinant 19
Level 19

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Lattice Invariants

Dimension:$2$
Determinant:$19$
Level:$19$
Label:$2.19.19.1.1$
Density:$0.360365392072833972695299029186\dots$
Group order:$4$
Hermite number:$0.458831467741123531814419156196\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rr} 2 & 1 \\ 1 & 10 \end{array}\right)$

Genus Structure

Class number:$1$
 
Genus representatives: $\left(\begin{array}{rr} 2 & 1 \\ 1 & 10 \end{array}\right)$
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