# Properties

 Label 2.173.aby_bli Base Field $\F_{173}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## 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:

• $y^2=104x^6+29x^5+33x^4+153x^3+33x^2+29x+104$
• $y^2=143x^6+75x^5+55x^4+103x^3+55x^2+75x+143$
• $y^2=28x^6+82x^5+169x^4+117x^3+40x^2+69x+26$
• $y^2=12x^6+94x^5+40x^4+109x^3+14x^2+2x+98$
• $y^2=18x^6+149x^5+130x^4+52x^3+130x^2+149x+18$
• $y^2=154x^6+18x^5+30x^4+21x^3+30x^2+18x+154$
• $y^2=172x^6+99x^5+83x^4+125x^3+83x^2+99x+172$
• $y^2=143x^6+99x^5+53x^4+79x^3+20x^2+46x+53$
• $y^2=66x^6+128x^5+139x^4+117x^3+55x^2+53x+102$
• $y^2=35x^6+29x^5+31x^4+40x^3+122x^2+164x+40$
• $y^2=69x^6+47x^5+78x^4+132x^3+78x^2+47x+69$
• $y^2=171x^6+73x^5+10x^4+65x^3+124x^2+21x+127$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22200 879120000 26780550708600 802321483392000000 24013782244908064851000 718709313575942719739280000 21510249615878209889184702449400 643780252191052224113280509952000000 19267699142657825629377465113749628623800 576662967585319386698212446158982784218000000

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)