# Properties

 Label 5.3.ac_b_c_m_abg Base Field $\F_{3}$ Dimension $5$ Ordinary No $p$-rank $5$

## Invariants

 Base field: $\F_{3}$ Dimension: $5$ Weil polynomial: $( 1 - 2 x^{2} + 9 x^{4} )( 1 - 2 x + 3 x^{2} - 2 x^{3} + 9 x^{4} - 18 x^{5} + 27 x^{6} )$ Frobenius angles: $\pm0.187977698232$, $\pm0.195913276015$, $\pm0.359846707444$, $\pm0.737803084298$, $\pm0.804086723985$ Angle rank: $4$ (numerical)

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $5$ Slopes: $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$

## Point counts

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 144 71424 17641584 7446380544 797373918864 230017182029568 53345113489489392 12023676621501235200 2979447860028439668816 701277720406485880391424

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 8 32 144 232 812 2326 6488 19850 57668

## Decomposition

2.3.a_ac $\times$ 3.3.ac_d_ac

## Base change

This is a primitive isogeny class.