Properties

Label 5.2.ai_bh_adm_ha_alc
Base Field $\F_{2}$
Dimension $5$
Ordinary No
$p$-rank $2$
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2}$
Dimension:  $5$
Weil polynomial:  $( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$
Frobenius angles:  $\pm0.174442860055$, $\pm0.25$, $\pm0.25$, $\pm0.25$, $\pm0.546783656212$
Angle rank:  $2$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 2 3500 136214 3500000 121438802 1668621500 23152725262 745038000000 31179508146098 1089154255437500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 7 19 39 75 91 79 159 451 987

Decomposition

1.2.ac 3 $\times$ 2.2.ac_d

Base change

This is a primitive isogeny class.