Properties

Label 3.454.908.15.15
Class number $15$
Dimension $3$
Determinant $454$
Level $908$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$454$
Level:$908$
Density:$0.556039541263669632805266740112\dots$
Group order:$2$
Hermite number:$1.04088968000657816472354251893\dots$
Minimal vector length:$8$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
Download this list for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 8 & 3 \\ 4 & 3 & 10 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$15$
 
$\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 8 & 3 \\ 4 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 4 & 2 \\ -1 & 2 & 66 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 10 & -2 \\ -1 & -2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & 0 \\ 1 & 0 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 8 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & -3 \\ 1 & -3 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 10 & -1 \\ 0 & -1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & -1 \\ 1 & 8 & 1 \\ -1 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 14 & -4 \\ 0 & -4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & 4 \\ 1 & 4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 14 & -5 \\ 0 & -5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 6 & 2 \\ 0 & 2 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 0 \\ -1 & 0 & 152 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 114 \end{array}\right)$
Download this list for gp, magma, sage

Comments

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