Integral Lattice 2.1.2.1.1 (Z2, I2)

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

This is the square lattice $\Z_2$.

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

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.