Properties

Label 3.9.ap_dv_aoo
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{4}( 1 - 3 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $0.0$, $0.0$, $\pm0.333333333333$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 112 372736 358269184 272097280000 201692843439472 148863517207035904 109169082904342022128 79729975638991175680000 58143828227562824728473856 42389004617725712561894895616

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 55 676 6319 57835 527068 4772035 43027039 387381124 3486607255

Decomposition

1.9.ag 2 $\times$ 1.9.ad

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^2}$.

SubfieldPrimitive Model
$\F_{3}$3.3.d_ad_as
$\F_{3}$3.3.ad_ad_s