Properties

Label 3.9.ap_dx_apa
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:  $( 1 - 3 x )^{2}( 1 - 5 x + 9 x^{2} )( 1 - 4 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.267720472801$
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
$A(\F_{q^r})$ 120 403200 387185760 287078400000 206672306220600 149931211814092800 109284182329062122040 79720850263722393600000 58139039283678212484624480 42389173896245330958730080000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 59 730 6671 59275 530864 4777075 43022111 387349210 3486621179

Decomposition

1.9.ag $\times$ 1.9.af $\times$ 1.9.ae

Base change

This is a primitive isogeny class.