Properties

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

Learn more about

Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 24 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$
Frobenius angles:  $\pm0.110906256499$, $\pm0.169471200781$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19880 695163840 18746811790280 498324695078246400 13239718531676564803400 351764130911272391032943040 9346015280265292556280303101480 248314266607559416625257100557516800 6597461725129958751217335184590995262440 175287960540280923251832377787965042067403200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26162 4328770 705930574 115064334598 18755382529154 3057125417782834 498311416260346846 81224760550450580950 13239635967102757019282

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ay $\times$ 1.163.aw 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.ac_ahu$2$(not in LMFDB)
2.163.c_ahu$2$(not in LMFDB)
2.163.bu_bgw$2$(not in LMFDB)