Properties

Label 3.3.ae_e_a
Base Field $\F_{3}$
Dimension $3$
$p$-rank $2$

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.073451917328$, $\pm0.166666666667$, $\pm0.740118583995$
Angle rank:  $1$ (numerical)

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4 336 11200 646464 14147284 406425600 11275287244 281074789632 7732512961600 206706589004496

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 2 12 98 240 764 2352 6530 19956 59282

Decomposition

1.3.ad $\times$ 2.3.ab_ac

Base change

This is a primitive isogeny class.