Properties

Label 2.17.ak_by
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.422020869623$
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
$A(\F_{q^r})$ 160 83200 24088480 6922240000 2011667984800 582622284524800 168396666261788320 48662075833712640000 14063067032705334535840 4064231406646822197280000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 290 4904 82878 1416808 24137570 410384584 6975884158 118587729608 2015993900450

Decomposition

1.17.ai $\times$ 1.17.ac

Base change

This is a primitive isogeny class.