Properties

Label 2.9.ai_bh
Base Field $\F_{3^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 - 3 x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 35 6825 580160 44342025 3500486675 282375475200 22878365334755 1853317902297225 150101800979654720 12157496427346895625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 84 794 6756 59282 531342 4783298 43053636 387438986 3486735924

Decomposition

1.9.af $\times$ 1.9.ad

Base change

This is a primitive isogeny class.