Properties

Label 2.163.abs_bfa
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:  $( 1 - 24 x + 163 x^{2} )( 1 - 20 x + 163 x^{2} )$
Frobenius angles:  $\pm0.110906256499$, $\pm0.213555132351$
Angle rank:  $2$ (numerical)
Jacobians:  90

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 90 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20160 697374720 18754040652480 498338451704217600 13239725573807133508800 351764071713685814346455040 9346015003898980334057004745920 248314265871108977884795916451840000 6597461723825601067523331718369267266240 175287960539255905238826389278224271165593600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26246 4330440 705950062 115064395800 18755379372854 3057125327382120 498311414782454878 81224760534391959480 13239635967025336611686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ay $\times$ 1.163.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ae_afy$2$(not in LMFDB)
2.163.e_afy$2$(not in LMFDB)
2.163.bs_bfa$2$(not in LMFDB)