Properties

Label 2.8.ac_d
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 2 x + 3 x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.183599693504$, $\pm0.661057072878$
Angle rank:  $2$ (numerical)
Number field:  4.0.730688.3
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 50 4300 243350 17372000 1092165250 68706952300 4404214182950 281573228144000 18009895480464050 1152884227313351500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 67 475 4239 33327 262099 2100091 16783071 134184175 1073707107

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.