Properties

Label 2.9.ah_bc
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:  $( 1 - 5 x + 9 x^{2} )( 1 - 2 x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.391826552031$
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
$A(\F_{q^r})$ 40 7200 574240 43574400 3486260200 282801715200 22903292926120 1853550571737600 150085285359054880 12156892273411380000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 89 786 6641 59043 532142 4788507 43059041 387396354 3486562649

Decomposition

1.9.af $\times$ 1.9.ac

Base change

This is a primitive isogeny class.