↑

Properties

Label 3.706.1412.19.10
Class number $19$
Dimension $3$
Determinant $706$
Level $1412$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$706$
Level:$1412$
Density:$0.157647198985701663086884385784\dots$
Group order:$2$
Hermite number:$0.449219318144587410008475882871\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 8 & 3 \\ 1 & 3 & 24 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$19$
 
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 8 & 3 \\ 1 & 3 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -1 \\ 0 & 8 & 3 \\ -1 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 14 & -2 \\ 1 & -2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 3 \\ 1 & 10 & -4 \\ 3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -3 \\ 3 & 10 & -4 \\ -3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 10 & -1 \\ 1 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & 5 \\ -1 & 5 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 10 & -4 \\ 2 & -4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -3 \\ 1 & 8 & -4 \\ -3 & -4 & 14 \end{array}\right)$ ...
Download the complete list for gp, magma, sage

Comments

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