Lattice Invariants
Dimension: | $3$ |
Determinant: | $310$ |
Level: | $620$ |
Density: | $0.0841129314300471436731192773188\dots$ |
Group order: | $8$ |
Hermite number: | $0.295512664476324720442338892656\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $4$ |
Normalized minimal vectors: |
|
Download this list for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 78 \end{array}\right)$
Genus Structure
Class number: | $8$ |
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 78 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -5 \\ 0 & -5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -4 \\ 0 & -4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & 0 \\ 1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 1 \\ 1 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 0 \\ -1 & 8 & 0 \\ 0 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 8 & -2 \\ 2 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 6 & -2 \\ 2 & -2 & 10 \end{array}\right)$ | |
Download this list for gp, magma, sage |
Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.