Properties

Label 2.163.abu_bgx
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:  $( 1 - 23 x + 163 x^{2} )^{2}$
Frobenius angles:  $\pm0.143017980409$, $\pm0.143017980409$
Angle rank:  $1$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19881 695218689 18747410509584 498328257515063481 13239733616627199559641 351764181157756594946754816 9346015416601942599610691534241 248314266904961255998581494146821609 6597461725597123709983336583287845605136 175287960540486808950011013697965826299530049

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 118 26164 4328908 705935620 115064465698 18755385208198 3057125462379190 498311416857166084 81224760556202090164 13239635967118307726164

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-123}) \)$)$
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_ahv$2$(not in LMFDB)
2.163.bu_bgx$2$(not in LMFDB)
2.163.x_oc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_ahv$2$(not in LMFDB)
2.163.bu_bgx$2$(not in LMFDB)
2.163.x_oc$3$(not in LMFDB)
2.163.a_hv$4$(not in LMFDB)
2.163.ax_oc$6$(not in LMFDB)