Properties

Label 3.48.96.2.2
Class number $2$
Dimension $3$
Determinant $48$
Level $96$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$48$
Level:$96$
Density:$0.213758305026977349257339393278\dots$
Group order:$8$
Hermite number:$0.550321208149104447312434992068\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 10 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 8 q^{10} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 22 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 3 \\ 1 & 3 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$2$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 3 \\ 1 & 3 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 2 & 0 \\ 0 & 0 & 16 \end{array}\right)$
Download this list for gp, magma, sage

Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.