Properties

Label 2.17.an_cy
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.24063253699$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 132 79200 24659712 7053552000 2021889165252 582896408371200 168380808657984516 48660354784857024000 14062989450255637909248 4064225418633377836476000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 273 5018 84449 1424005 24148926 410345941 6975637441 118587075386 2015990930193

Decomposition

1.17.ah $\times$ 1.17.ag

Base change

This is a primitive isogeny class.