Properties

Label 3.3.ah_x_abw
Base Field $\F_{3}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0540867239847$, $\pm0.166666666667$, $\pm0.445913276015$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 2 476 17528 420784 13355422 417166400 11113784362 283090010112 7513685815496 205054047616796

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 7 24 63 227 784 2321 6575 19392 58807

Decomposition

1.3.ad $\times$ 2.3.ae_i

Base change

This is a primitive isogeny class.