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Properties

Label 3.238.476.7.1
Class number $7$
Dimension $3$
Determinant $238$
Level $476$

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Lattice Invariants

Dimension:$3$
Determinant:$238$
Level:$476$
Density:$0.0959964421273544504541430137376\dots$
Group order:$12$
Hermite number:$0.322728765445643764502241814763\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 80 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$7$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 80 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 10 & -4 \\ 1 & -4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -1 \\ 0 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & -5 \\ 0 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 8 & 1 \\ 1 & 1 & 8 \end{array}\right)$
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Comments

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