Properties

Label 2.163.abr_bec
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:  $( 1 - 24 x + 163 x^{2} )( 1 - 19 x + 163 x^{2} )$
Frobenius angles:  $\pm0.110906256499$, $\pm0.232879815243$
Angle rank:  $2$ (numerical)
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20300 698401200 18756862938800 498341452495320000 13239717154708875582500 351764020207227936776428800 9346014864051384567920721737300 248314265660177081872110754708320000 6597461723847830045607080983504249242800 175287960540469755117365559799342320381630000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26285 4331092 705954313 115064322631 18755376626630 3057125281637317 498311414359161553 81224760534665631916 13239635967117019636925

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ay $\times$ 1.163.at 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.af_afa$2$(not in LMFDB)
2.163.f_afa$2$(not in LMFDB)
2.163.br_bec$2$(not in LMFDB)