Properties

Label 2.17.al_cg
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.381477984739$
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
$A(\F_{q^r})$ 150 81900 24242400 6945120000 2011609803750 582452363001600 168388692037314150 48662783705128320000 14063149824404621522400 4064231032629148100947500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 285 4936 83153 1416767 24130530 410365151 6975985633 118588427752 2015993714925

Decomposition

1.17.ai $\times$ 1.17.ad

Base change

This is a primitive isogeny class.