Properties

Label 3.1492.2984.13.1
Class number 13
Dimension 3
Determinant 1492
Level 2984

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Lattice Invariants

Dimension:$3$
Determinant:$1492$
Level:$2984$
Label:$3.1492.2984.13.1$
Density:$0.0383406264210621849074951898116\dots$
Group order:$16$
Hermite number:$0.175027808314567874329348916683\dots$
Minimal vector length:$2$
Kissing Number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 4q^{18} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 374 \end{array}\right)$

Genus Structure

Class number:$13$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 374 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 18 & 1 \\ 1 & 1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 14 & -4 \\ -2 & -4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 20 & -2 \\ 1 & -2 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & -2 \\ -2 & 14 & 3 \\ -2 & 3 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 3 & -4 \\ 3 & 10 & -1 \\ -4 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 26 & -11 \\ 0 & -11 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 14 & -1 \\ 1 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 10 & -1 \\ 2 & -1 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 14 & 6 \\ -1 & 6 & 58 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 0 \\ 2 & 18 & 1 \\ 0 & 1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 26 & -2 \\ 1 & -2 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 498 \end{array}\right)$
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Comments

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