Properties

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

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Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 9 x^{2} )( 1 - 9 x + 37 x^{2} - 81 x^{3} + 81 x^{4} )$
Frobenius angles:  $\pm0.114191348093$, $\pm0.309392441858$, $\pm0.333333333333$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 203 551551 432188624 290257574607 205178835835568 149539215667825984 109362993987711290267 79800135562291241304207 58166139676492021765391696 42394545487999492284379058176

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 84 811 6740 58843 529473 4780522 43064900 387529759 3487062999

Decomposition

1.9.ad $\times$ 2.9.aj_bl

Base change

This is a primitive isogeny class.