Properties

Label 3.1898.3796.23.2
Class number 23
Dimension 3
Determinant 1898
Level 3796

Learn more about

Lattice Invariants

Dimension:$3$
Determinant:$1898$
Level:$3796$
Label:$3.1898.3796.23.2$
Density:$0.0339934710031979402102518200809\dots$
Group order:$4$
Hermite number:$0.161534240093199093394485875969\dots$
Minimal vector length:$2$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 20 & 9 \\ 1 & 9 & 52 \end{array}\right)$

Genus Structure

Class number:$23$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 20 & 9 \\ 1 & 9 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 5 \\ 1 & 5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 18 & 5 \\ 2 & 5 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & -1 \\ 0 & 12 & -1 \\ -1 & -1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 12 & 5 \\ 1 & 5 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & -2 \\ 3 & 10 & -2 \\ -2 & -2 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 22 & -9 \\ 1 & -9 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -2 \\ 1 & 12 & 4 \\ -2 & 4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 3 & -1 \\ 3 & 14 & 4 \\ -1 & 4 & 16 \end{array}\right)$ ...
Download the complete list for gp, magma, sage

Comments

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