Properties

Label 4.3.ai_bg_adg_gj
Base Field $\F_{3}$
Dimension $4$
$p$-rank $2$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{3}$
Dimension:  $4$
Weil polynomial:  $( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$
Frobenius angles:  $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.254551732336$, $\pm0.538152604671$
Angle rank:  $2$ (numerical)

Newton polygon

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

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 7889 680512 54662881 5079693647 343587786752 23073342565007 1827315445641777 150688359407419456 12108904870630602209

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 10 32 102 336 874 2208 6470 19760 58810

Decomposition

1.3.ad 2 $\times$ 2.3.ac_f

Base change

This is a primitive isogeny class.