Properties

Label 2.9.af_w
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 9 x^{2} )( 1 - x + 9 x^{2} )$
Frobenius angles:  $\pm0.267720472801$, $\pm0.446699620962$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 54 8316 585144 43243200 3479436054 282591783936 22876761836934 1852381109779200 150075137632452984 12157840428622265916

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 101 800 6593 58925 531746 4782965 43031873 387370160 3486834581

Decomposition

1.9.ae $\times$ 1.9.ab

Base change

This is a primitive isogeny class.