↑

Properties

Label 3.1658.3316.40.6
Class number $40$
Dimension $3$
Determinant $1658$
Level $3316$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$1658$
Level:$3316$
Density:$0.0363706742913891381440696254686\dots$
Group order:$4$
Hermite number:$0.168979940786991289807772998441\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 18 & 2 \\ 1 & 2 & 48 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$40$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 18 & 2 \\ 1 & 2 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 18 & 9 \\ 1 & 9 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -4 \\ 1 & 12 & -6 \\ -4 & -6 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 18 & -9 \\ -2 & -9 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 5 & 4 \\ 5 & 12 & -1 \\ 4 & -1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & -1 \\ 1 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 20 & 1 \\ 2 & 1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 14 & 4 \\ 2 & 4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 16 & 7 \\ -2 & 7 & 30 \end{array}\right)$ ...
Download the complete list for gp, magma, sage

Comments

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