Properties

Label 2.17.al_cf
Base Field $\F_{17}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0363222529514$, $\pm0.389420801446$
Angle rank:  $2$ (numerical)
Number field:  4.0.44573.1
Galois group:  $D_{4}$
Jacobians:  1

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 149 81205 24077357 6923944325 2009816552704 582322075016005 168377063814286973 48661568906378867525 14063040965304164776373 4064223610137057085542400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 283 4903 82899 1415502 24125131 410336815 6975811491 118587509791 2015990033118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.44573.1.
All geometric endomorphisms are defined over $\F_{17}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.l_cf$2$(not in LMFDB)