Properties

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

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$
Frobenius angles:  $0.0$, $0.0$, $\pm0.384973271919$, $1.0$, $1.0$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 8 686 1296 21142 134456 2290318 14580000 135260678 893968328

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9
$C(\F_{q^r})$ 2 14 22 24 142 224 518 840 1982

Decomposition

1.2.ab $\times$ 2.2.a_ae

Base change

This is a primitive isogeny class.