Properties

Name A5
Label 5.6.12.1.1
Class number 1
Dimension 5
Determinant 6
Level 12

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Lattice Invariants

Dimension:$5$
Determinant:$6$
Level:$12$
Label:$5.6.12.1.1$
Density:$0.379881250517603758105399396698\dots$
Group order:$1440$
Hermite number:$1.39765423754315849046595420554\dots$
Minimal vector length:$2$
Kissing Number:$30$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(1, 1, 0, 0, 0)$, $(1, 1, 1, 0, 0)$, $(1, 1, 1, 1, 0)$, $(1, 1, 1, 1, 1)$, $(0, 1, 0, 0, 0)$, $(0, 1, 1, 0, 0)$, $(0, 1, 1, 1, 0)$, $(0, 1, 1, 1, 1)$, $(0, 0, 1, 0, 0)$, $(0, 0, 1, 1, 0)$, $(0, 0, 1, 1, 1)$, $(0, 0, 0, 1, 0)$, $(0, 0, 0, 1, 1)$, $(0, 0, 0, 0, 1)$ ...
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut +\mathstrut 90q^{4} \) \(\mathstrut +\mathstrut 140q^{6} \) \(\mathstrut +\mathstrut 270q^{8} \) \(\mathstrut +\mathstrut 360q^{10} \) \(\mathstrut +\mathstrut 330q^{12} \) \(\mathstrut +\mathstrut 660q^{14} \) \(\mathstrut +\mathstrut 810q^{16} \) \(\mathstrut +\mathstrut 570q^{18} \) \(\mathstrut +\mathstrut 1020q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 2 \end{array}\right)$

Genus Structure

Class number:$1$
 
Genus representatives: $\left(\begin{array}{rrrrr} 2 & -1 & -1 & -1 & -1 \\ -1 & 2 & 1 & 1 & 1 \\ -1 & 1 & 2 & 1 & 1 \\ -1 & 1 & 1 & 2 & 1 \\ -1 & 1 & 1 & 1 & 2 \end{array}\right)$
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Comments

This integral lattice is the A5 lattice.

This is a root lattice.