Properties

Name Z2, I2
Label 2.1.2.1.1
Class number 1
Dimension 2
Determinant 1
Level 2

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Lattice Invariants

Dimension:$2$
Determinant:$1$
Level:$2$
Label:$2.1.2.1.1$
Density:$0.785398163397448309615660845820\dots$
Group order:$8$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing Number:$4$
Normalized minimal vectors: $(1, 0)$, $(0, 1)$
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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

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

Genus Structure

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

This integral lattice is the Z2, I2 lattice.

This is the square lattice Z2.