# Properties

 Label 2.173.abw_bji 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: $( 1 - 26 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$ Frobenius angles: $\pm0.0485897903475$, $\pm0.184705758688$ Angle rank: $2$ (numerical) Jacobians: 22

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 22 curves, and hence is principally polarizable:

• $y^2=76x^6+169x^5+16x^4+104x^3+16x^2+169x+76$
• $y^2=108x^6+92x^5+74x^4+43x^3+6x^2+66x+141$
• $y^2=171x^6+32x^5+127x^4+4x^3+127x^2+32x+171$
• $y^2=112x^6+142x^5+125x^4+136x^3+14x^2+163x+44$
• $y^2=91x^6+83x^5+27x^4+131x^3+104x^2+85x+131$
• $y^2=164x^6+52x^5+133x^4+151x^3+133x^2+52x+164$
• $y^2=169x^6+22x^5+5x^4+9x^3+93x^2+96x+122$
• $y^2=104x^6+48x^5+88x^4+170x^3+88x^2+48x+104$
• $y^2=127x^6+93x^5+118x^4+124x^3+169x^2+166x+112$
• $y^2=21x^6+96x^5+88x^4+28x^3+94x^2+105x+59$
• $y^2=85x^6+119x^5+5x^4+50x^3+5x^2+119x+85$
• $y^2=50x^6+113x^5+52x^4+49x^3+52x^2+113x+50$
• $y^2=51x^5+27x^4+27x^3+50x^2+107x+140$
• $y^2=69x^6+22x^5+165x^4+142x^3+154x^2+x+150$
• $y^2=163x^6+129x^5+86x^4+32x^3+137x^2+160x+82$
• $y^2=3x^6+147x^5+83x^4+124x^3+33x^2+93x+143$
• $y^2=98x^6+96x^5+156x^4+37x^3+156x^2+96x+98$
• $y^2=122x^6+37x^5+133x^4+32x^3+132x^2+18x+19$
• $y^2=111x^6+146x^5+24x^4+41x^3+136x^2+138x+91$
• $y^2=140x^6+157x^5+158x^4+107x^3+158x^2+157x+140$
• $y^2=31x^6+137x^5+122x^4+77x^3+122x^2+137x+31$
• $y^2=48x^6+170x^5+71x^4+170x^3+71x^2+170x+48$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22496 881843200 26791611942368 802351808075776000 24013838193176195292896 718709347851569200874675200 21510249377949692766897778641632 643780250893341497769386853629952000 19267699138466758790823869494176152318432 576662967575189765445824505866046442658176000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 126 29462 5174406 895736814 154964087886 26808756787334 4637914343365590 802359177988171486 138808137860248950558 24013807852322386420982

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.aba $\times$ 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ae_ais $2$ (not in LMFDB) 2.173.e_ais $2$ (not in LMFDB) 2.173.bw_bji $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ae_ais $2$ (not in LMFDB) 2.173.e_ais $2$ (not in LMFDB) 2.173.bw_bji $2$ (not in LMFDB) 2.173.aba_qs $4$ (not in LMFDB) 2.173.as_jy $4$ (not in LMFDB) 2.173.s_jy $4$ (not in LMFDB) 2.173.ba_qs $4$ (not in LMFDB)