Properties

Label 2.173.abw_bjl
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:  $( 1 - 25 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$
Frobenius angles:  $\pm0.100717649571$, $\pm0.161302001611$
Angle rank:  $2$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22499 882028297 26793852469184 802366691511310249 24013909377830444581499 718709620770779195096190976 21510250259274684069083418603107 643780253342292483478066856771740425 19267699144328431169197885890430967316416 576662967586972484667162796438715362456479577

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 29468 5174838 895753428 154964547246 26808766967558 4637914533391734 802359181040359396 138808137902477543694 24013807852813050762668

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.az $\times$ 1.173.ax 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ac_aiv$2$(not in LMFDB)
2.173.c_aiv$2$(not in LMFDB)
2.173.bw_bjl$2$(not in LMFDB)