Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 - 4 x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.267720472801$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30 6300 572760 44856000 3528999150 282897619200 22869516972990 1852525706976000 150082272164810520 12157508118174457500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 77 784 6833 59761 532322 4781449 43035233 387388576 3486739277

Decomposition

1.9.af $\times$ 1.9.ae

Base change

This is a primitive isogeny class.