# Properties

 Label 2.9.ag_bb Base Field $\F_{3^2}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{3^2}$ Dimension: $2$ Weil polynomial: $( 1 - 3 x + 9 x^{2} )^{2}$ Frobenius angles: $\pm0.333333333333$, $\pm0.333333333333$ Angle rank: $0$ (numerical)

## Newton polygon

This isogeny class is supersingular.

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

## Point counts

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 49 8281 614656 44129449 3458263249 280883040256 22855886093089 1853585177078089 150125140011540736 12158077251781589401

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 100 838 6724 58564 528526 4778596 43059844 387499222 3486902500

## Decomposition

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^2}$.
 Subfield Primitive Model $\F_{3}$ 2.3.g_p $\F_{3}$ 2.3.a_ad $\F_{3}$ 2.3.ag_p