Properties

Label 2.17.ai_bi
Base Field $\F_{17}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 17 x^{2} )( 1 + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.5$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 180 84240 23636340 6900940800 2014849494900 582835555345680 168380213909806260 48660468604600320000 14063132835209808916020 4064241540180178760317200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 294 4810 82622 1419050 24146406 410344490 6975653758 118588284490 2015998927014

Decomposition

1.17.ai $\times$ 1.17.a

Base change

This is a primitive isogeny class.