# Properties

 Label 3.3.ag_v_abs Base Field $\F_{3}$ Dimension $3$ $p$-rank $3$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{3}$ Dimension: $3$ Weil polynomial: $( 1 - 2 x + 3 x^{2} )^{3}$ Frobenius angles: $\pm0.304086723985$, $\pm0.304086723985$, $\pm0.304086723985$ Angle rank: $1$ (numerical)

## Newton polygon

This isogeny class is ordinary.

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

## 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 1728 54872 884736 14172488 320013504 9287485208 278189309952 7849750559624 210984921816768

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 16 58 124 238 592 1930 6460 20254 60496

1.3.ac 3

## Base change

This is a primitive isogeny class.