Properties

Label 3.9.am_cu_aki
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 4 x + 9 x^{2} )( 1 - 8 x + 31 x^{2} - 72 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.0954872438962$, $\pm0.267720472801$, $\pm0.376614839446$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 198 534996 420216984 286629456960 205017018156918 149771811162625344 109418724723460909878 79786721933346727031040 58155430818098028926587032 42392272897104319363555272276

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 82 790 6658 58798 530296 4782958 43057666 387458422 3486876082

Decomposition

1.9.ae $\times$ 2.9.ai_bf

Base change

This is a primitive isogeny class.