Properties

Label 2.8.ai_bf
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:  $( 1 - 5 x + 8 x^{2} )( 1 - 3 x + 8 x^{2} )$
Frobenius angles:  $\pm0.154919815756$, $\pm0.322067999368$
Angle rank:  $2$ (numerical)

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
$A(\F_{q^r})$ 24 4032 283464 17305344 1078754424 68718476736 4399672453032 281608132377600 18018366420234456 1152964797368674752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 63 553 4223 32921 262143 2097929 16785151 134247289 1073782143

Decomposition

1.8.af $\times$ 1.8.ad

Base change

This is a primitive isogeny class.