Properties

Label 2.9.ag_x
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:  $( 1 - 5 x + 9 x^{2} )( 1 - x + 9 x^{2} )$
Frobenius angles:  $\pm0.186429498677$, $\pm0.446699620962$
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
$A(\F_{q^r})$ 45 7425 559440 42953625 3493462725 283568947200 22908121480485 1852906027883625 150071331224742480 12157247924912660625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 92 766 6548 59164 533582 4789516 43044068 387360334 3486664652

Decomposition

1.9.af $\times$ 1.9.ab

Base change

This is a primitive isogeny class.