Properties

Label 3.3.ae_j_aq
Base Field $\F_{3}$
Dimension $3$
$p$-rank $3$

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x + 3 x^{2} )( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.116139763599$, $\pm0.304086723985$, $\pm0.616139763599$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8 960 16568 614400 16708648 363833280 10174091992 294794035200 7793263245896 207571534104000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 12 24 92 280 684 2128 6844 20112 59532

Decomposition

1.3.ac $\times$ 2.3.ac_c

Base change

This is a primitive isogeny class.