Properties

Label 2.163.abr_bed
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $1 - 43 x + 783 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.118291691051$, $\pm0.228958314505$
Angle rank:  $2$ (numerical)
Number field:  4.0.10730853.1
Galois group:  $D_{4}$
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20301 698455905 18757422458343 498344464171420125 13239728212946730397296 351764050229122747237392105 9346014923199659725682107416867 248314265725856010253172120341267125 6597461723778287839698176849614542086337 175287960539847764355146293470807837655238400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26287 4331221 705958579 115064418736 18755378227339 3057125300984995 498311414490964531 81224760533809461883 13239635967070040190982

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.10730853.1.
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

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