Properties

Label 2.173.abw_bjm
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:  $( 1 - 24 x + 173 x^{2} )^{2}$
Frobenius angles:  $\pm0.134271185755$, $\pm0.134271185755$
Angle rank:  $1$ (numerical)
Jacobians:  39

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 39 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22500 882090000 26794599322500 802371645504000000 24013932957293468062500 718709710112381370219210000 21510250540458302770593295522500 643780254081975313572514612224000000 19267699145892077385283975716465781222500 576662967589178786731288173916267438982250000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 29470 5174982 895758958 154964699406 26808770300110 4637914594018902 802359181962244318 138808137913742345886 24013807852904927156350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-29}) \)$)$
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.a_aiw$2$(not in LMFDB)
2.173.bw_bjm$2$(not in LMFDB)
2.173.y_pn$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.a_aiw$2$(not in LMFDB)
2.173.bw_bjm$2$(not in LMFDB)
2.173.y_pn$3$(not in LMFDB)
2.173.a_iw$4$(not in LMFDB)
2.173.ay_pn$6$(not in LMFDB)