Properties

Label 2.9.af_s
Base Field $\F_{3^2}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.5$
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
$A(\F_{q^r})$ 50 7500 540200 42720000 3514951250 283929120000 22888831190450 1852470606720000 150086550606213800 12157702312129687500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 93 740 6513 59525 534258 4785485 43033953 387399620 3486794973

Decomposition

1.9.af $\times$ 1.9.a

Base change

This is a primitive isogeny class.