Properties

Label 3.3.af_o_abb
Base Field $\F_{3}$
Dimension $3$
Ordinary No
$p$-rank $2$
Contains a Jacobian No

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Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.254551732336$, $\pm0.538152604671$
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
$A(\F_{q^r})$ 7 1127 24304 600691 18744257 438249728 10168947803 275073828939 7655372861584 205909243298087

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 13 32 93 309 820 2127 6389 19760 59053

Decomposition

1.3.ad $\times$ 2.3.ac_f

Base change

This is a primitive isogeny class.