Properties

Label 3.3.ag_s_abk
Base Field $\F_{3}$
Dimension $3$
$p$-rank $0$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.5$
Angle rank:  $0$ (numerical)

Newton polygon

This isogeny class is supersingular.

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

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
$A(\F_{q^r})$ 4 784 21952 529984 17919604 481890304 11264613868 282428473600 7626759805504 205891160792464

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 10 28 82 298 892 2350 6562 19684 59050

Decomposition

1.3.ad 2 $\times$ 1.3.a

Base change

This is a primitive isogeny class.