# Properties

 Label 3.4.ai_bf_acy Base Field $\F_{2^2}$ Dimension $3$ $p$-rank $2$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{2^2}$ Dimension: $3$ Weil polynomial: $( 1 - 2 x )^{2}( 1 - 3 x + 4 x^{2} )( 1 - x + 4 x^{2} )$ Frobenius angles: $0.0$, $0.0$, $\pm0.230053456163$, $\pm0.419569376745$ 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 $A(\F_{q^r})$ 8 3456 275576 15552000 1002369128 67500687744 4373112673112 278319151872000 17822595334324424 1147521271227129216

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 15 69 239 957 4023 16293 64799 259341 1043655

## Decomposition

1.4.ae $\times$ 1.4.ad $\times$ 1.4.ab

## Base change

This is a primitive isogeny class.