# Properties

 Label 3.3.aj_bk_add Base Field $\F_{3}$ Dimension $3$ Ordinary No $p$-rank $0$ Contains a Jacobian No

## Invariants

 Base field: $\F_{3}$ Dimension: $3$ Weil polynomial: $( 1 - 3 x + 3 x^{2} )^{3}$ Frobenius angles: $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$ Angle rank: $0$ (numerical)

## Newton polygon

This isogeny class is supersingular.

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

## 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 $A(\F_{q^r})$ 1 343 21952 753571 19902511 481890304 11681631109 293151929707 7626759805504 203370086883943

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 1 28 109 325 892 2431 6805 19684 58321