↑

Properties

Label 3.220.440.5.3
Class number $5$
Dimension $3$
Determinant $220$
Level $440$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$220$
Level:$440$
Density:$0.282408177995436045462084235670\dots$
Group order:$4$
Hermite number:$0.662601524943923985314776144584\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 6 q^{16} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 14 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 0 \\ 1 & 0 & 14 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$5$
 
$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 4 & 0 \\ 1 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 8 & -3 \\ -1 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 8 & 2 \\ 1 & 2 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & -1 \\ -1 & -1 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & -2 \\ 2 & 6 & -1 \\ -2 & -1 & 12 \end{array}\right)$
Download this list for gp, magma, sage

Comments

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