Properties

Name A2
Label 2.3.3.1.1
Class number 1
Dimension 2
Determinant 3
Level 3

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Lattice Invariants

Dimension:$2$
Determinant:$3$
Level:$3$
Label:$2.3.3.1.1$
Density:$0.906899682117108925297039128820\dots$
Group order:$12$
Hermite number:$1.15470053837925152901829756100\dots$
Minimal vector length:$2$
Kissing Number:$6$
Normalized minimal vectors: $(1, 0)$, $(1, 1)$, $(0, 1)$
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Theta Series

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

Gram Matrix

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

Genus Structure

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

This integral lattice is the A2 lattice.

This is a root lattice.