# Properties

 Label 5.2.ag_r_abg_bx_acs Base Field $\F_{2}$ Dimension $5$ Ordinary No $p$-rank $4$ Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $5$ Weil polynomial: $( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ Frobenius angles: $\pm0.0516399385854$, $\pm0.123548644961$, $\pm0.25$, $\pm0.456881978294$, $\pm0.718306605252$ Angle rank: $2$ (numerical)

## Newton polygon

 $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 1 665 15808 1107225 29590151 1177379840 45108385589 917031425625 32442795501376 1266342321457325

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 3 3 19 27 69 165 211 471 1143

## Decomposition

1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_ab

## Base change

This is a primitive isogeny class.