Properties

Label 3.9.am_ct_ake
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:  $( 1 - 3 x )^{2}( 1 - 4 x + 9 x^{2} )( 1 - 2 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.267720472801$, $\pm0.391826552031$
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
$A(\F_{q^r})$ 192 516096 406021824 280756224000 203349578004672 149363904526147584 109295760482674730688 79742356910436777984000 58141681205855497715964096 42389092453345368814267785216

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 80 766 6524 58318 528848 4777582 43033724 387366814 3486614480

Decomposition

1.9.ag $\times$ 1.9.ae $\times$ 1.9.ac

Base change

This is a primitive isogeny class.