↑

Properties

Label 3.734.1468.20.18
Class number $20$
Dimension $3$
Determinant $734$
Level $1468$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$734$
Level:$1468$
Density:$0.284038668373728020934635160946\dots$
Group order:$2$
Hermite number:$0.665149440969666371200726099330\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 6 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 10 & 4 \\ 1 & 4 & 14 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$20$
 
$\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 10 & 4 \\ 1 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & -3 \\ 1 & -3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & -1 \\ 0 & -1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 14 & -6 \\ -1 & -6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 184 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 8 & -1 \\ -1 & -1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 14 & 3 \\ 0 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 6 & 3 \\ -2 & 3 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & -1 \\ -1 & -1 & 106 \end{array}\right)$ ...
Download the complete list for gp, magma, sage

Comments

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