Properties

Label 3.9.am_cv_akm
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:  $(1-4x+9x^{2})(1-8x+32x^{2}-72x^{3}+81x^{4})$
Frobenius angles:  $\pm0.141826552031$, $\pm0.267720472801$, $\pm0.358173447969$
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
$A(\F_{q^r})$ 204 554064 434556108 292368491520 206409655841964 149959581944847696 109428947791245977196 79788845613454165278720 58156407117240050479084812 42391916971192988358669313104

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 84 814 6788 59198 530964 4783406 43058812 387464926 3486846804

Decomposition

1.9.ae $\times$ 2.9.ai_bg

Base change

This is a primitive isogeny class.