# Properties

 Label 4.2.af_m_au_bd Base Field $\F_{2}$ Dimension $4$ Ordinary No $p$-rank $4$ Contains a Jacobian No

## Invariants

 Base field: $\F_{2}$ Dimension: $4$ Weil polynomial: $1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8}$ Frobenius angles: $\pm0.0635622003031$, $\pm0.165221137389$, $\pm0.365221137389$, $\pm0.663562200303$ Angle rank: $2$ (numerical) Number field: 8.0.13140625.1 Galois group: $C_2^2:C_4$

This isogeny class is simple.

## Newton polygon

This isogeny class is ordinary.

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

## 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 $A(\F_{q^r})$ 1 211 1861 88831 1046771 12172801 344358281 5598573775 68193052891 1095729526441

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 4 4 20 33 46 159 324 508 1019

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.