# Properties

 Label 3.3.ag_r_abh Base Field $\F_{3}$ Dimension $3$ Ordinary No $p$-rank $2$ Contains a Jacobian No

## Invariants

 Base field: $\F_{3}$ Dimension: $3$ Weil polynomial: $( 1 - 3 x + 3 x^{2} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$ Frobenius angles: $\pm0.0975263560046$, $\pm0.166666666667$, $\pm0.527857038681$ Angle rank: $2$ (numerical)

## Newton polygon

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

## 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 $A(\F_{q^r})$ 3 567 15372 449631 16923408 453228048 10841393181 285987347919 7805622152412 207827302701312

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 8 19 68 283 845 2266 6644 20143 59603

## Decomposition

1.3.ad $\times$ 2.3.ad_f

## Base change

This is a primitive isogeny class.