# Properties

 Label 2.9.af_s Base Field $\F_{3^2}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{3^2}$ Dimension: $2$ Weil polynomial: $( 1 - 5 x + 9 x^{2} )( 1 + 9 x^{2} )$ Frobenius angles: $\pm0.186429498677$, $\pm0.5$ Angle rank: $1$ (numerical)

## Newton polygon

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

## Point counts

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 50 7500 540200 42720000 3514951250 283929120000 22888831190450 1852470606720000 150086550606213800 12157702312129687500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 93 740 6513 59525 534258 4785485 43033953 387399620 3486794973

## Decomposition

1.9.af $\times$ 1.9.a

## Base change

This is a primitive isogeny class.