↑

Properties

Label 5.20736.24.1.3
Class number $1$
Dimension $5$
Determinant $20736$
Level $24$

Downloads

Learn more

Lattice Invariants

Dimension:$5$
Determinant:$20736$
Level:$24$
Density:$0.0638573679162815547174301193362\dots$
Group order:$72$
Hermite number:$0.684896595632177400961874140096\dots$
Minimal vector length:$5$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{5} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 2 q^{9} \) \(\mathstrut +\mathstrut 6 q^{12} \) \(\mathstrut +\mathstrut 12 q^{17} \) \(\mathstrut +\mathstrut 36 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 5 & -1 & 1 & 1 & -1 \\ -1 & 5 & 1 & 1 & -1 \\ 1 & 1 & 5 & -1 & 1 \\ 1 & 1 & -1 & 17 & 7 \\ -1 & -1 & 1 & 7 & 17 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 5 & -1 & 1 & 1 & -1 \\ -1 & 5 & 1 & 1 & -1 \\ 1 & 1 & 5 & -1 & 1 \\ 1 & 1 & -1 & 17 & 7 \\ -1 & -1 & 1 & 7 & 17 \end{array}\right)$
Download this matrix for gp, magma, sage