Lattice Invariants
Dimension: | $3$ |
Determinant: | $478$ |
Level: | $956$ |
Density: | $0.541900628227981876353833063299\dots$ |
Group order: | $2$ |
Hermite number: | $1.02316895613975021476583123234\dots$ |
Minimal vector length: | $8$ |
Kissing number: | $4$ |
Normalized minimal vectors: |
|
Download this list for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 8 & 0 \\ 3 & 0 & 10 \end{array}\right)$
Genus Structure
Class number: | $18$ |
$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 8 & 0 \\ 3 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 8 & -4 \\ -2 & -4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 8 & 3 \\ 1 & 3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 1 \\ 0 & 1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 1 \\ 0 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 8 & -3 \\ -1 & -3 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 14 & 2 \\ 0 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 16 & -7 \\ 0 & -7 & 18 \end{array}\right)$ ... | |
Download the complete list for gp, magma, sage |
Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.