Properties

Label 5.2.ah_bc_acy_ga_ajo
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:  $( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$
Frobenius angles:  $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.384973271919$, $\pm0.5$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 6 9000 276822 2250000 50036646 1245699000 26430987246 738112500000 29572112791494 1135206406125000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 12 26 32 46 72 94 160 422 1032

Decomposition

1.2.ac 3 $\times$ 1.2.ab $\times$ 1.2.a

Base change

This is a primitive isogeny class.