Properties

Label 3.2.ad_e_ae
Base Field $\F_{2}$
Dimension $3$
$p$-rank $1$

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.139386741866$, $\pm0.25$, $\pm0.686170398078$
Angle rank:  $2$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 80 338 10400 57482 256880 2525098 16660800 124272122 1161136400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 4 6 32 50 64 154 256 474 1104

Decomposition

1.2.ac $\times$ 2.2.ab_a

Base change

This is a primitive isogeny class.