Properties

Label 2.173.abu_bhi
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:  $( 1 - 26 x + 173 x^{2} )( 1 - 20 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.225058830207$
Angle rank:  $2$ (numerical)
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22792 884329600 26799941496328 802366253860864000 24013832366865170070472 718709211891008664601475200 21510248847137557929528484527688 643780249628334982866154613145600000 19267699136803332855078348111026017545352 576662967576536666818134472099765715706448000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29546 5176016 895752942 154964050288 26808751715834 4637914228914976 802359176411562718 138808137848265316448 24013807852378475042186

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ag_ags$2$(not in LMFDB)
2.173.g_ags$2$(not in LMFDB)
2.173.bu_bhi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ag_ags$2$(not in LMFDB)
2.173.g_ags$2$(not in LMFDB)
2.173.bu_bhi$2$(not in LMFDB)
2.173.ay_qk$4$(not in LMFDB)
2.173.aq_kg$4$(not in LMFDB)
2.173.q_kg$4$(not in LMFDB)
2.173.y_qk$4$(not in LMFDB)