Properties

Label 2.17.ao_df
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:  $( 1 - 7 x + 17 x^{2} )^{2}$
Frobenius angles:  $\pm0.177280642489$, $\pm0.177280642489$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 121 75625 24285184 7035015625 2022342812281 583087267840000 168401996374543129 48661783896050015625 14063036162888693026816 4064222751691998577515625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 260 4942 84228 1424324 24156830 410397572 6975842308 118587469294 2015989607300

Decomposition

1.17.ah 2

Base change

This is a primitive isogeny class.