# Properties

 Label 3.2.ac_e_ag Base Field $\F_{2}$ Dimension $3$ Ordinary No $p$-rank $0$

## Invariants

 Base field: $\F_{2}$ Dimension: $3$ Weil polynomial: $1 - 2 x + 4 x^{2} - 6 x^{3} + 8 x^{4} - 8 x^{5} + 8 x^{6}$ Frobenius angles: $\pm0.159385776661$, $\pm0.421684666515$, $\pm0.635759575232$ Angle rank: $3$ (numerical) Number field: 6.0.503792.1 Galois group: $S_4\times C_2$

This isogeny class is simple.

## Newton polygon

 $p$-rank: $0$ Slopes: $[1/3, 1/3, 1/3, 2/3, 2/3, 2/3]$

## Point counts

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 5 185 395 4625 40025 277685 2851945 21538625 120507785 978891425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 9 7 17 41 69 169 321 457 929

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.