Properties

Label 2.173.abu_bhq
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:  $( 1 - 24 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$
Frobenius angles:  $\pm0.134271185755$, $\pm0.184705758688$
Angle rank:  $2$ (numerical)
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22800 884822400 26805666358800 802401972083712000 24013988905912734234000 718709744388026762386646400 21510250302529775421369242278800 643780252784264583416961360052224000 19267699141701010546026872886127142672400 576662967579049165478832439672975291934832000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29562 5177120 895792814 154965060448 26808771578634 4637914542718144 802359180344875486 138808137883549110080 24013807852483102291482

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ay $\times$ 1.173.aw 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_aha$2$(not in LMFDB)
2.173.c_aha$2$(not in LMFDB)
2.173.bu_bhq$2$(not in LMFDB)