Properties

Label 3.9.ao_dn_anj
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:  $( 1 - 5 x + 9 x^{2} )( 1 - 9 x + 37 x^{2} - 81 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.114191348093$, $\pm0.186429498677$, $\pm0.309392441858$
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
$A(\F_{q^r})$ 145 454575 407933140 291655774575 207683952643600 150333772543732800 109470554778010749265 79788628908046762340175 58157096944618521111886420 42392520185198133737402880000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 68 767 6772 59561 532289 4785224 43058692 387469523 3486896423

Decomposition

1.9.af $\times$ 2.9.aj_bl

Base change

This is a primitive isogeny class.