Properties

Label 2.17.aj_bw
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:  $( 1 - 7 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.422020869623$
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
$A(\F_{q^r})$ 176 88000 24679424 6978400000 2015978955056 582878636032000 168406364743212464 48661929864662400000 14062994505410958119936 4064222670497930690200000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 305 5022 83553 1419849 24148190 410408217 6975863233 118587118014 2015989567025

Decomposition

1.17.ah $\times$ 1.17.ac

Base change

This is a primitive isogeny class.