Properties

Label 2.17.ak_cc
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:  $1 - 10 x + 54 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.159208333631$, $\pm0.39120422124$
Angle rank:  $2$ (numerical)
Number field:  4.0.23600.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 164 85936 24686756 6986253056 2015353294564 582747563627056 168404709712798436 48663022317189017600 14063096205542845055204 4064224265858270698670896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 298 5024 83646 1419408 24142762 410404184 6976019838 118587975608 2015990358378

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.