Properties

Label 5.2.ah_y_aca_dg_aeq
Base Field $\F_{2}$
Dimension $5$
$p$-rank $1$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - 2 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.139386741866$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.686170398078$
Angle rank:  $2$ (numerical)

Newton polygon

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

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 2000 57122 6500000 96627242 1085318000 32242976362 843453000000 28751722418042 1219918930250000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 4 14 48 66 64 122 192 410 1104

Decomposition

1.2.ac 3 $\times$ 2.2.ab_a

Base change

This is a primitive isogeny class.