Properties

Label 3.1212.2424.18.15
Class number 18
Dimension 3
Determinant 1212
Level 2424

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Lattice Invariants

Dimension:$3$
Determinant:$1212$
Level:$2424$
Label:$3.1212.2424.18.15$
Density:$0.475605986397417879577661603595\dots$
Group order:$2$
Hermite number:$0.937919992725400471593176595833\dots$
Minimal vector length:$10$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 10 & 4 & 1 \\ 4 & 12 & 2 \\ 1 & 2 & 12 \end{array}\right)$

Genus Structure

Class number:$18$
 
Genus representatives: $\left(\begin{array}{rrr} 10 & 4 & 1 \\ 4 & 12 & 2 \\ 1 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 12 & 3 \\ 0 & 3 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 12 & -1 \\ 1 & -1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & 1 \\ -3 & 12 & 2 \\ 1 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 12 & 2 & 6 \\ 2 & 12 & -1 \\ 6 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -2 \\ 0 & 8 & 3 \\ -2 & 3 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & -2 \\ -3 & 12 & 0 \\ -2 & 0 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -1 & -3 \\ -1 & 12 & -3 \\ -3 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 2 \\ -2 & 12 & 3 \\ 2 & 3 & 30 \end{array}\right)$ ...
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Comments

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