# Properties

 Label 5.3.am_cu_aks_bdf_acgq Base Field $\F_{3}$ Dimension $5$ $p$-rank $3$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{3}$ Dimension: $5$ Weil polynomial: $(1-3x+3x^{2})^{2}(1-2x+3x^{2})^{3}$ Frobenius angles: $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$ Angle rank: $1$ (numerical)

## Newton polygon

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1]$

## Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8 84672 43019648 7326498816 1040841691208 196698220314624 47815326632944088 12276340965871976448 3041463221467834454144 729641401212067086359232

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -8 10 58 142 292 700 2092 6622 20254 60010

## Decomposition

1.3.ad 2 $\times$ 1.3.ac 3

## Base change

This is a primitive isogeny class.