# Properties

 Label 3.2.ac_f_ai Base Field $\F_{2}$ Dimension $3$ $p$-rank $2$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{2}$ Dimension: $3$ Weil polynomial: $( 1 + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ Frobenius angles: $\pm0.174442860055$, $\pm0.5$, $\pm0.546783656212$ Angle rank: $2$ (numerical)

## Newton polygon

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

## 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 $A(\F_{q^r})$ 6 252 558 2016 58146 492156 2069934 14716800 143731314 1101401532

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 11 7 7 51 107 127 223 547 1051

## Decomposition

1.2.a $\times$ 2.2.ac_d

## Base change

This is a primitive isogeny class.