Properties

Label 2.173.abx_bki
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:  $( 1 - 26 x + 173 x^{2} )( 1 - 23 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.161302001611$
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
$A(\F_{q^r})$ 22348 880511200 26786438306368 802338869747056000 24013819842264500046748 718709362328292594266675200 21510249575846558479031011278364 643780251671997729825680312313792000 19267699140557827182194136000578810746432 576662967579202210278480231449120091710476000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 125 29417 5173406 895722369 154963969465 26808757327334 4637914386034957 802359178958629921 138808137875313401558 24013807852489475491457

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ad_ajs$2$(not in LMFDB)
2.173.d_ajs$2$(not in LMFDB)
2.173.bx_bki$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ad_ajs$2$(not in LMFDB)
2.173.d_ajs$2$(not in LMFDB)
2.173.bx_bki$2$(not in LMFDB)
2.173.abb_qw$4$(not in LMFDB)
2.173.at_ju$4$(not in LMFDB)
2.173.t_ju$4$(not in LMFDB)
2.173.bb_qw$4$(not in LMFDB)