Properties

Label 2.17.ak_cf
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:  $1 - 10 x + 57 x^{2} - 170 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.216316574334$, $\pm0.35680475752$
Angle rank:  $2$ (numerical)
Number field:  4.0.94784.1
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
$A(\F_{q^r})$ 167 88009 25138844 7030951001 2016631399207 582548565889936 168376961566020983 48661465336673635049 14063068252832495135516 4064225203064888872883449

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 304 5114 84180 1420308 24134518 410336564 6975796644 118587739898 2015990823264

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.