Properties

Label 2.17.an_cw
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.292637436158$
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
$A(\F_{q^r})$ 130 77740 24261640 6990380800 2015239733650 582427647143680 168363781664704210 48661076024196480000 14063166150216570691720 4064241387720474658254700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 269 4940 83697 1419325 24129506 410304445 6975740833 118588565420 2015998851389

Decomposition

1.17.ai $\times$ 1.17.af

Base change

This is a primitive isogeny class.