Properties

Label 2.17.am_cs
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:  $( 1 - 6 x + 17 x^{2} )^{2}$
Frobenius angles:  $\pm0.24063253699$, $\pm0.24063253699$
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
$A(\F_{q^r})$ 144 82944 25040016 7072137216 2021435619984 582705611375616 168359623607186064 48658925715634520064 14062942737777746304144 4064228085576507141325824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 286 5094 84670 1423686 24141022 410294310 6975432574 118586681478 2015992253086

Decomposition

1.17.ag 2

Base change

This is a primitive isogeny class.