Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )$
Frobenius angles:  $\pm0.115026728081$, $\pm0.384973271919$, $\pm0.884973271919$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 32 1036 4096 23804 306656 2314316 23887872 135273628 1133260832

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 2 14 14 22 74 142 350 518 1082

Decomposition

1.2.ab $\times$ 2.2.a_ad

Base change

This is a primitive isogeny class.