Properties

Label 3.9.ao_dj_amm
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:  $( 1 - 3 x )^{4}( 1 - 2 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.391826552031$
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
$A(\F_{q^r})$ 128 393216 354613376 267386880000 200873135078528 149088223639240704 109288030313761926272 79739985108381204480000 58137430693349635276548224 42386898140942813132882313216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 60 668 6204 57596 527868 4777244 43032444 387338492 3486433980

Decomposition

1.9.ag 2 $\times$ 1.9.ac

Base change

This is a primitive isogeny class.