Properties

Label 3.758.1516.19.11
Class number 19
Dimension 3
Determinant 758
Level 1516

Learn more about

Lattice Invariants

Dimension:$3$
Determinant:$758$
Level:$1516$
Label:$3.758.1516.19.11$
Density:$0.152143711484287999918659009107\dots$
Group order:$2$
Hermite number:$0.438702648315186715273823555310\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 3 \\ 1 & 3 & 22 \end{array}\right)$

Genus Structure

Class number:$19$
 
Genus representatives: $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 3 \\ 1 & 3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 190 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 2 & -4 \\ 2 & 10 & -3 \\ -4 & -3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 10 & -5 \\ 1 & -5 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 6 & -1 \\ 1 & -1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 0 \\ 1 & 10 & 2 \\ 0 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -4 & 4 \\ -4 & 10 & -5 \\ 4 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & 2 \\ 3 & 10 & 3 \\ 2 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 10 & -2 \\ 1 & -2 & 20 \end{array}\right)$ ...
Download the complete list for gp, magma, sage

Comments

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