Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 + x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.553300379038$
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
$A(\F_{q^r})$ 55 7425 520960 42953625 3536439775 283568947200 22869540900415 1852906027883625 150101769987685120 12157247924912660625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 92 714 6548 59886 533582 4781454 43044068 387438906 3486664652

Decomposition

1.9.af $\times$ 1.9.b

Base change

This is a primitive isogeny class.