Properties

Label 2.17.aq_du
Base Field $\F_{17}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 100 67600 23136100 6922240000 2013702902500 582574494096400 168382600473360100 48662075833712640000 14063181218281174560100 4064240224008909221290000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 230 4706 82878 1418242 24135590 410350306 6975884158 118588692482 2015998274150

Decomposition

1.17.ai 2

Base change

This is a primitive isogeny class.