Lattice Invariants
Dimension: | $3$ |
Determinant: | $310$ |
Level: | $620$ |
Density: | $0.237907296798661686277268626453\dots$ |
Group order: | $4$ |
Hermite number: | $0.591025328952649440884677785312\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
Download this vector for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 10 \end{array}\right)$
Genus Structure
Class number: | $8$ |
$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & 4 \\ 0 & 4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & -2 \\ 3 & 8 & -4 \\ -2 & -4 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 78 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 1 \\ 1 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 2 \\ 1 & 6 & 2 \\ 2 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -5 \\ 0 & -5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & 0 \\ 1 & 0 & 16 \end{array}\right)$ | |
Download this list for gp, magma, sage |
Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.