Properties

Label 3.2.ae_k_ar
Base Field $\F_{2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $3$
Weil polynomial:  $( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.123548644961$, $\pm0.384973271919$, $\pm0.456881978294$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2 152 1064 2736 21142 323456 3131242 20142432 135386552 1078157432

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 9 14 9 19 78 181 305 518 1029

Decomposition

1.2.ab $\times$ 2.2.ad_f

Base change

This is a primitive isogeny class.