Lattice Invariants
Dimension: | $3$ |
Determinant: | $446$ |
Level: | $892$ |
Density: | $0.0701255348166987686198554233288\dots$ |
Group order: | $4$ |
Hermite number: | $0.261769097745826690902456187389\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 16 & 5 \\ 0 & 5 & 16 \end{array}\right)$
Genus Structure
Class number: | $13$ |
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 16 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 14 & 1 \\ 0 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 0 \\ -1 & 8 & -2 \\ 0 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 10 & -5 \\ 1 & -5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 10 & 2 \\ 1 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 4 \\ 1 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 1 \\ 0 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 0 \\ -1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 112 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 64 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 8 & 3 \\ -1 & 3 & 16 \end{array}\right)$ | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.