Properties

Label 3.9.aq_eh_aqq
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{4}( 1 - 4 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.267720472801$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 96 344064 353699424 275251200000 203335689903456 149138782586486784 109126861026819003744 79695895293906124800000 58136263494505804643289696 42389045379616655062460350464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 48 666 6396 58314 528048 4770186 43008636 387330714 3486610608

Decomposition

1.9.ag 2 $\times$ 1.9.ae

Base change

This is a primitive isogeny class.