# Properties

 Label 2.27.ao_du 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: $1 - 14 x + 98 x^{2} - 378 x^{3} + 729 x^{4}$ Frobenius angles: $\pm0.151580709202$, $\pm0.348419290798$ Angle rank: $1$ (numerical) Number field: $$\Q(i, \sqrt{5})$$ Galois group: $V_4$

This isogeny class is simple.

## 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 $A(\F_{q^r})$ 436 531920 392133604 282938886400 205894948939556 150094634644128080 109420681608829356404 79766914395414351974400 58149792769259473116882196 42391158275216613267267698000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 14 730 19922 532398 14349174 387420490 10460515002 282431205278 7625604798014 205891132094650

## Decomposition

This is a simple isogeny class.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^3}$.

 Subfield Primitive Model $\F_{3}$ 2.3.ac_c