Properties

Label 2.17.al_ch
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:  $1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.106224360187$, $\pm0.372781387459$
Angle rank:  $2$ (numerical)
Number field:  4.0.185661.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 151 82597 24407791 6965983189 2013247390576 582546874152541 168394948323913903 48663393247233584325 14063201274021632223919 4064233266062100403793152

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 287 4969 83403 1417922 24134447 410380397 6976073011 118588861603 2015994822782

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.185661.1.
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_ch$2$(not in LMFDB)