Properties

Label 2.173.aby_bli
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:  $( 1 - 26 x + 173 x^{2} )( 1 - 24 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.134271185755$
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
$A(\F_{q^r})$ 22200 879120000 26780550708600 802321483392000000 24013782244908064851000 718709313575942719739280000 21510249615878209889184702449400 643780252191052224113280509952000000 19267699142657825629377465113749628623800 576662967585319386698212446158982784218000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 124 29370 5172268 895702958 154963726844 26808755508810 4637914394666348 802359179605540318 138808137890442186364 24013807852744211285850

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 1.173.ay 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.ac_aks$2$(not in LMFDB)
2.173.c_aks$2$(not in LMFDB)
2.173.by_bli$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ac_aks$2$(not in LMFDB)
2.173.c_aks$2$(not in LMFDB)
2.173.by_bli$2$(not in LMFDB)
2.173.abc_ra$4$(not in LMFDB)
2.173.au_jq$4$(not in LMFDB)
2.173.u_jq$4$(not in LMFDB)
2.173.bc_ra$4$(not in LMFDB)