Properties

Label 3.1886.3772.27.16
Class number 27
Dimension 3
Determinant 1886
Level 3772

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Lattice Invariants

Dimension:$3$
Determinant:$1886$
Level:$3772$
Label:$3.1886.3772.27.16$
Density:$0.0964534497246906838846851659965\dots$
Group order:$4$
Hermite number:$0.323752225041188651959101294525\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 22 & -1 \\ 1 & -1 & 22 \end{array}\right)$

Genus Structure

Class number:$27$
 
Genus representatives: $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 22 & -1 \\ 1 & -1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 22 & -8 \\ 2 & -8 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -2 & -2 \\ -2 & 16 & -7 \\ -2 & -7 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 5 & 4 \\ 5 & 14 & 2 \\ 4 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 18 & 8 \\ 1 & 8 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 2 \\ -1 & 10 & -3 \\ 2 & -3 & 50 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 4 \\ -3 & 16 & 0 \\ 4 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & -2 \\ -4 & 14 & 3 \\ -2 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 0 \\ 0 & 0 & 82 \end{array}\right)$ ...
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.