Properties

Label 2.173.abt_bgo
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:  $( 1 - 25 x + 173 x^{2} )( 1 - 20 x + 173 x^{2} )$
Frobenius angles:  $\pm0.100717649571$, $\pm0.225058830207$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 22946 885853276 26807359396664 802394076574685056 24013921902477812598986 718709470333441169314014976 21510249530565660366886889391194 643780251298629731216236286312640000 19267699140573936841347359972443508920376 576662967584306941206781120088883579780214396

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29597 5177448 895784001 154964628069 26808761356058 4637914376271753 802359178493292193 138808137875429458584 24013807852702050313397

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.az $\times$ 1.173.au 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.af_afy$2$(not in LMFDB)
2.173.f_afy$2$(not in LMFDB)
2.173.bt_bgo$2$(not in LMFDB)