# Properties

 Label 2.27.ao_dq Base Field $\F_{3^3}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

## Invariants

 Base field: $\F_{3^3}$ Dimension: $2$ Weil polynomial: $( 1 - 10 x + 27 x^{2} )( 1 - 4 x + 27 x^{2} )$ Frobenius angles: $\pm0.0877398280459$, $\pm0.374235869875$ Angle rank: $2$ (numerical)

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 432 525312 388788336 282088341504 205770439178352 150084962864833536 109420525804631796144 79766921119469941555200 58149787206719839230617904 42391159674417632728167293952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 14 722 19754 530798 14340494 387395522 10460500106 282431229086 7625604068558 205891138890482

## Decomposition

1.27.ak $\times$ 1.27.ae

## Base change

This is a primitive isogeny class.