↑

Properties

Label 3.214.428.8.2
Class number $8$
Dimension $3$
Determinant $214$
Level $428$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$214$
Level:$428$
Density:$0.101236408398101545904223000774\dots$
Group order:$12$
Hermite number:$0.334368536666564844245461743752\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 72 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$8$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 72 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 1 \\ -1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 6 & -2 \\ 0 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 0 \\ 1 & 0 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 1 \\ -1 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & -3 \\ 1 & 6 & 1 \\ -3 & 1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 18 \end{array}\right)$
Download this list for gp, magma, sage

Comments

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