Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 - 4 x + 9 x^{2} )( 1 - 3 x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.267720472801$, $\pm0.333333333333$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 210 573300 449043840 297978408000 207529853014050 149931211814092800 109334197962682051170 79757313527212802208000 58150855561130292346485120 42391327562335941209352832500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 86 838 6914 59518 530864 4779262 43041794 387427942 3486798326

Decomposition

1.9.af $\times$ 1.9.ae $\times$ 1.9.ad

Base change

This is a primitive isogeny class.