↑

Properties

Label 3.428.856.10.3
Class number $10$
Dimension $3$
Determinant $428$
Level $856$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$428$
Level:$856$
Density:$0.202472816796203091808446001547\dots$
Group order:$4$
Hermite number:$0.530776966849572511888961784206\dots$
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

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

Gram Matrix

$\left(\begin{array}{rrr} 4 & 0 & 2 \\ 0 & 4 & 1 \\ 2 & 1 & 28 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$10$
 
$\left(\begin{array}{rrr} 4 & 0 & 2 \\ 0 & 4 & 1 \\ 2 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 4 & -1 \\ 1 & -1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 2 \\ 0 & 12 & -5 \\ 2 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 6 & -1 \\ 2 & -1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 10 & 3 \\ 1 & 3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 10 & -1 \\ 0 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 10 & -1 \\ -2 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 4 \\ 0 & 4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 8 & 1 \\ 2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 1 \\ -1 & 1 & 108 \end{array}\right)$
Download this list for gp, magma, sage

Comments

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