Properties

Label 2.173.abt_bgi
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:  $( 1 - 26 x + 173 x^{2} )( 1 - 19 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.243098056104$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22940 885484000 26803159497920 802368664178800000 24013814791080017410700 718709122145939889392896000 21510248621391612523301006523980 643780249376632240926433263652800000 19267699137346231482604127263731989946560 576662967580188447544570545779478078405100000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29585 5176638 895755633 154963936869 26808748368230 4637914180240953 802359176097859393 138808137852176460534 24013807852530545082425

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 1.173.at 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.ah_afs$2$(not in LMFDB)
2.173.h_afs$2$(not in LMFDB)
2.173.bt_bgi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ah_afs$2$(not in LMFDB)
2.173.h_afs$2$(not in LMFDB)
2.173.bt_bgi$2$(not in LMFDB)
2.173.ax_qg$4$(not in LMFDB)
2.173.ap_kk$4$(not in LMFDB)
2.173.p_kk$4$(not in LMFDB)
2.173.x_qg$4$(not in LMFDB)