Properties

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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1 97 2689 67609 457601 19040809 323696297 4570976881 73309284673 955259018737

Point counts of the (virtual) curve

$r$ 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.