↑

Properties

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

Downloads

Learn more

This is the square lattice $\Z^2$.

Lattice Invariants

Dimension:$2$
Determinant:$1$
Level:$2$
Density:$0.785398163397448309615660845820\dots$
Group order:$8$
Hermite number:$1.00000000000000000000000000000\dots$
Minimal vector length:$1$
Kissing number:$4$
Normalized minimal vectors: $(1, 0)$, $(0, 1)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q \) \(\mathstrut +\mathstrut 4 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 8 q^{5} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{9} \) \(\mathstrut +\mathstrut 8 q^{10} \) \(\mathstrut +\mathstrut 8 q^{13} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 8 q^{17} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right)$
Download this matrix for gp, magma, sage

Comments

This integral lattice is the Z2, I2 lattice.

This is the square lattice Z2.