↑

Properties

Label 6.12.12.1.1
Class number $1$
Dimension $6$
Determinant $12$
Level $12$

Downloads

Learn more

Lattice Invariants

Dimension:$6$
Determinant:$12$
Level:$12$
Density:$0.186473772791032469781738779340\dots$
Group order:$2880$
Hermite number:$1.32180215216672942822786467645\dots$
Minimal vector length:$2$
Kissing number:$32$
Normalized minimal vectors: $(1, 0, 0, -1, 0, 0)$, $(1, 0, 0, 0, 0, 0)$, $(1, 1, 0, -1, -1, 0)$, $(1, 1, 0, -1, 0, 0)$, $(1, 1, 1, -1, -1, 0)$, $(0, 1, 0, -1, -1, 0)$, $(0, 1, 0, -1, 0, 0)$, $(0, 1, 0, 0, -1, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 1, 1, -1, -1, 0)$, $(0, 1, 1, 0, -1, 0)$, $(0, 0, 1, 0, -1, 0)$, $(0, 0, 1, 0, 0, 0)$, $(0, 0, 0, 1, 0, 0)$, $(0, 0, 0, 0, 1, 0)$, $(0, 0, 0, 0, 0, 1)$ ...
Download the complete list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 32 q^{2} \) \(\mathstrut +\mathstrut 150 q^{4} \) \(\mathstrut +\mathstrut 320 q^{6} \) \(\mathstrut +\mathstrut 552 q^{8} \) \(\mathstrut +\mathstrut 960 q^{10} \) \(\mathstrut +\mathstrut 1230 q^{12} \) \(\mathstrut +\mathstrut 1600 q^{14} \) \(\mathstrut +\mathstrut 2670 q^{16} \) \(\mathstrut +\mathstrut 2912 q^{18} \) \(\mathstrut +\mathstrut 2880 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrrr} 2 & 0 & 0 & 1 & 0 & 0 \\ 0 & 2 & 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 & 1 & 0 \\ 1 & 1 & 0 & 2 & 0 & 0 \\ 0 & 1 & 1 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrrr} 2 & 0 & 0 & -1 & -1 & 0 \\ 0 & 2 & -1 & 0 & 1 & 0 \\ 0 & -1 & 2 & 0 & -1 & 0 \\ -1 & 0 & 0 & 2 & 1 & 0 \\ -1 & 1 & -1 & 1 & 2 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 \end{array}\right)$
Download this matrix for gp, magma, sage