Properties

Label 2.17.ak_cg
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $( 1 - 6 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$
Frobenius angles:  $\pm0.24063253699$, $\pm0.338793663197$
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
$A(\F_{q^r})$ 168 88704 25290216 7045226496 2016775051368 582428009471616 168362197932856872 48660773969287839744 14063094298249656917544 4064231720210425246353024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 306 5144 84350 1420408 24129522 410300584 6975697534 118587959528 2015994055986

Decomposition

1.17.ag $\times$ 1.17.ae

Base change

This is a primitive isogeny class.