Properties

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

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 2 x - x^{2} - 16 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.122567728653$, $\pm0.694307243617$
Angle rank:  $2$ (numerical)
Number field:  4.0.6208.2
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
$A(\F_{q^r})$ 46 3772 232162 17170144 1078988926 68667483388 4409034052882 281588781946752 18015139030071022 1153044167785947772

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 59 451 4191 32927 261947 2102387 16783999 134223247 1073856059

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.