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Properties

Label 3.1270.2540.21.16
Class number $21$
Dimension $3$
Determinant $1270$
Level $2540$

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Lattice Invariants

Dimension:$3$
Determinant:$1270$
Level:$2540$
Density:$0.332454137548330402798392887443\dots$
Group order:$2$
Hermite number:$0.738735120831535913032341095360\dots$
Minimal vector length:$8$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 2 & 3 \\ 2 & 10 & 2 \\ 3 & 2 & 18 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$21$
 
$\left(\begin{array}{rrr} 8 & 2 & 3 \\ 2 & 10 & 2 \\ 3 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & -2 \\ 1 & -2 & 86 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & -2 \\ 0 & 10 & 3 \\ -2 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & -4 \\ -4 & 12 & 3 \\ -4 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & 1 \\ 1 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & -3 \\ -1 & -3 & 68 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 0 \\ -1 & 12 & -5 \\ 0 & -5 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 8 & 1 \\ -2 & 1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 16 & -4 \\ 0 & -4 & 42 \end{array}\right)$ ...
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Comments

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