Properties

Label 3.9.ao_dm_ane
Base Field $\F_{3^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x )^{2}( 1 - 5 x + 9 x^{2} )( 1 - 3 x + 9 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.186429498677$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 140 436800 392188160 283788960000 205002501634700 149654483848396800 109326465075198903980 79754941280297861760000 58146604377922946565505280 42389133134230805094692520000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 66 740 6594 58796 529884 4778924 43040514 387399620 3486617826

Decomposition

1.9.ag $\times$ 1.9.af $\times$ 1.9.ad

Base change

This is a primitive isogeny class.