Properties

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

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.0975263560046$, $\pm0.304086723985$, $\pm0.527857038681$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 6 972 20862 474336 15112416 395418348 10043458998 281036490624 7880965995582 210389494182912

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 13 29 73 254 745 2099 6529 20333 60328

Decomposition

1.3.ac $\times$ 2.3.ad_f

Base change

This is a primitive isogeny class.