# Properties

 Label 4.3.al_cf_agy_oo Base Field $\F_{3}$ Dimension $4$ $p$-rank $1$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{3}$ Dimension: $4$ Weil polynomial: $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ Frobenius angles: $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.304086723985$ Angle rank: $1$ (numerical)

## Newton polygon

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

## 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 $A(\F_{q^r})$ 2 4116 834176 72342816 4816407662 329612967936 24554788591118 1913695797127296 151574224374586496 12107028012374894676

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -7 3 38 123 323 846 2345 6771 19874 58803

## Decomposition

1.3.ad 3 $\times$ 1.3.ac

## Base change

This is a primitive isogeny class.