# Properties

 Label 4.2.ae_g_ae_c Base Field $\F_{2}$ Dimension $4$ $p$-rank $0$ Does not contain a Jacobian

## Invariants

 Base field: $\F_{2}$ Dimension: $4$ Weil polynomial: $1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8}$ Frobenius angles: $\pm0.0377785699724$, $\pm0.148391828106$, $\pm0.398391828106$, $\pm0.787778569972$ Angle rank: $2$ (numerical) Number field: 8.0.18939904.2 Galois group: $D_4\times C_2$

This isogeny class is simple.

## Newton polygon

 $p$-rank: $0$ Slopes: $[1/4, 1/4, 1/4, 1/4, 3/4, 3/4, 3/4, 3/4]$

## 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 97 2689 67609 457601 19040809 323696297 4570976881 73309284673 955259018737

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 1 5 17 9 73 153 273 545 881

## Decomposition

This is a simple isogeny class.

## Base change

This is a primitive isogeny class.