Properties

Label 2.163.abw_bis
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:  $( 1 - 24 x + 163 x^{2} )^{2}$
Frobenius angles:  $\pm0.110906256499$, $\pm0.110906256499$
Angle rank:  $1$ (numerical)
Jacobians:  14

This isogeny class is not 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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19600 692742400 18737297395600 498298198325760000 13239662582857049290000 351764049369583674937657600 9346015256458778963967678691600 248314266959430677226754206965760000 6597461726709980907866463679260940531600 175287960544900297010000085190495207353760000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 116 26070 4326572 705893038 115063848356 18755378181510 3057125409995612 498311416966474078 81224760569903050196 13239635967451661911350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_ajq$2$(not in LMFDB)
2.163.bw_bis$2$(not in LMFDB)
2.163.y_px$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_ajq$2$(not in LMFDB)
2.163.bw_bis$2$(not in LMFDB)
2.163.y_px$3$(not in LMFDB)
2.163.a_jq$4$(not in LMFDB)
2.163.ay_px$6$(not in LMFDB)