Properties

Label 2.8.ae_l
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:  $( 1 - 5 x + 8 x^{2} )( 1 + x + 8 x^{2} )$
Frobenius angles:  $\pm0.154919815756$, $\pm0.556567041129$
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
$A(\F_{q^r})$ 40 4480 248920 16576000 1092104200 69112140160 4398152090680 281554963200000 18018521584662760 1152896258924502400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 71 485 4047 33325 263639 2097205 16781983 134248445 1073718311

Decomposition

1.8.af $\times$ 1.8.b

Base change

This is a primitive isogeny class.