Properties

Label 2.173.abw_bji
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.184705758688$
Angle rank:  $2$ (numerical)
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22496 881843200 26791611942368 802351808075776000 24013838193176195292896 718709347851569200874675200 21510249377949692766897778641632 643780250893341497769386853629952000 19267699138466758790823869494176152318432 576662967575189765445824505866046442658176000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 29462 5174406 895736814 154964087886 26808756787334 4637914343365590 802359177988171486 138808137860248950558 24013807852322386420982

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 1.173.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 $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ae_ais$2$(not in LMFDB)
2.173.e_ais$2$(not in LMFDB)
2.173.bw_bji$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ae_ais$2$(not in LMFDB)
2.173.e_ais$2$(not in LMFDB)
2.173.bw_bji$2$(not in LMFDB)
2.173.aba_qs$4$(not in LMFDB)
2.173.as_jy$4$(not in LMFDB)
2.173.s_jy$4$(not in LMFDB)
2.173.ba_qs$4$(not in LMFDB)