Properties

Label 3.9.am_cm_aio
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:  $( 1 - 3 x )^{2}( 1 - 6 x + 19 x^{2} - 54 x^{3} + 81 x^{4} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.076305209342$, $\pm0.490896535327$
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
$A(\F_{q^r})$ 164 422464 342348032 265011667200 203356956658724 150033931905335296 109349577745059581828 79726722125738718643200 58145595477798964419045632 42392155970238647155349698624

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 66 640 6146 58318 531228 4779934 43025282 387392896 3486866466

Decomposition

1.9.ag $\times$ 2.9.ag_t

Base change

This is a primitive isogeny class.