Properties

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

Learn more about

Invariants

Base field:  $\F_{3^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 9 x^{2} )( 1 - 5 x + 9 x^{2} )^{2}$
Frobenius angles:  $\pm0.186429498677$, $\pm0.186429498677$, $\pm0.391826552031$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 200 540000 424937600 290859120000 207519638405000 150676753858560000 109603364748553368200 79789930477881347520000 58142982515689424071145600 42387155161569636007837500000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 82 796 6754 59518 533500 4791022 43059394 387375484 3486455122

Decomposition

1.9.af 2 $\times$ 1.9.ac

Base change

This is a primitive isogeny class.