Lattice Invariants
Dimension: | $3$ |
Determinant: | $1212$ |
Level: | $2424$ |
Density: | $0.475605986397417879577661603595\dots$ |
Group order: | $2$ |
Hermite number: | $0.937919992725400471593176595833\dots$ |
Minimal vector length: | $10$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 10 & 4 & 1 \\ 4 & 12 & 2 \\ 1 & 2 & 12 \end{array}\right)$
Genus Structure
Class number: | $18$ |
$\left(\begin{array}{rrr} 10 & 4 & 1 \\ 4 & 12 & 2 \\ 1 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 12 & 3 \\ 0 & 3 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 12 & -1 \\ 1 & -1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & 1 \\ -3 & 12 & 2 \\ 1 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 12 & 2 & 6 \\ 2 & 12 & -1 \\ 6 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -2 \\ 0 & 8 & 3 \\ -2 & 3 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -2 \\ -3 & 12 & 0 \\ -2 & 0 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -1 & -3 \\ -1 & 12 & -3 \\ -3 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 2 \\ -2 & 12 & 3 \\ 2 & 3 & 30 \end{array}\right)$ ... | |
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Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.