Properties

Label 3.9.an_dd_als
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:  $( 1 - 5 x + 9 x^{2} )( 1 - 8 x + 32 x^{2} - 72 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.141826552031$, $\pm0.186429498677$, $\pm0.358173447969$
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
$A(\F_{q^r})$ 170 494700 415467080 290410666800 207241756299850 150478121417299200 109578953846357944090 79811455760670936268800 58154932076137583398981640 42389851031258164123323067500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 75 780 6743 59437 532800 4789957 43071007 387455100 3486676875

Decomposition

1.9.af $\times$ 2.9.ai_bg

Base change

This is a primitive isogeny class.