Properties

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

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.24063253699$
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
$A(\F_{q^r})$ 120 74880 24069240 6996787200 2017565556600 582640049047680 168371111648329080 48660500749182566400 14063061977523943296120 4064234154788176529846400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 258 4900 83774 1420964 24138306 410322308 6975658366 118587686980 2015995263618

Decomposition

1.17.ai $\times$ 1.17.ag

Base change

This is a primitive isogeny class.