Properties

Label 3.9.an_dc_aln
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 9 x^{2} )( 1 - 8 x + 31 x^{2} - 72 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.0954872438962$, $\pm0.186429498677$, $\pm0.376614839446$
Angle rank:  $3$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 165 477675 401757840 284710063275 205843504466325 150289701349708800 109568716764711823245 79809331478766097628475 58153955801757775232225040 42390206939823698886979516875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 73 756 6613 59037 532132 4789509 43069861 387448596 3486706153

Decomposition

1.9.af $\times$ 2.9.ai_bf

Base change

This is a primitive isogeny class.