Properties

Label 2.8.ae_t
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 8 x^{2} )( 1 - x + 8 x^{2} )$
Frobenius angles:  $\pm0.322067999368$, $\pm0.443432958871$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 48 5760 299088 16704000 1060603248 68586860160 4399563506064 281487322368000 18014243112564912 1152961215197788800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 87 581 4079 32365 261639 2097877 16777951 134216573 1073778807

Decomposition

1.8.ad $\times$ 1.8.ab

Base change

This is a primitive isogeny class.