# Properties

 Label 3.3.ae_k_at Base Field $\F_{3}$ Dimension $3$ $p$-rank $3$

## Invariants

 Base field: $\F_{3}$ Dimension: $3$ Weil polynomial: $1 - 4 x + 10 x^{2} - 19 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6}$ Frobenius angles: $\pm0.125412673718$, $\pm0.335294135736$, $\pm0.5848234043$ Angle rank: $3$ (numerical) Number field: 6.0.11822771.1 Galois group: The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## Point counts

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9 1143 18981 545211 15988419 378462159 10238103549 297262667475 7912278137664 206324103862143

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 14 27 82 270 713 2142 6898 20412 59174

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.