Properties

 Label 2.173.abt_bgi 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: $( 1 - 26 x + 173 x^{2} )( 1 - 19 x + 173 x^{2} )$ Frobenius angles: $\pm0.0485897903475$, $\pm0.243098056104$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=30x^6+32x^5+154x^4+75x^3+146x^2+39x+16$
• $y^2=87x^6+99x^5+91x^4+8x^3+88x^2+171x+1$
• $y^2=155x^6+89x^5+96x^4+145x^3+151x^2+138x+28$
• $y^2=38x^6+107x^5+34x^4+71x^3+96x^2+28x+110$
• $y^2=167x^6+37x^5+160x^4+135x^3+156x^2+41x+71$
• $y^2=49x^6+2x^5+108x^4+73x^3+35x^2+61x+69$
• $y^2=54x^6+165x^5+83x^4+43x^3+42x^2+171$
• $y^2=98x^6+9x^5+82x^4+79x^3+69x^2+133x+108$
• $y^2=9x^6+133x^5+114x^4+24x^3+38x^2+143x+111$
• $y^2=70x^6+28x^5+95x^4+148x^3+25x^2+57x+21$
• $y^2=158x^6+119x^5+58x^4+2x^3+166x^2+121x+103$
• $y^2=114x^6+34x^5+139x^4+36x^3+40x^2+52x+148$
• $y^2=8x^6+26x^5+95x^4+30x^3+157x^2+115x+40$
• $y^2=11x^6+107x^4+124x^3+133x^2+37x+117$
• $y^2=166x^6+42x^5+115x^4+155x^3+17x^2+105x+165$
• $y^2=117x^6+54x^5+51x^4+116x^3+23x^2+161x+92$
• $y^2=12x^6+106x^5+56x^4+82x^3+5x^2+157x+49$
• $y^2=138x^6+159x^5+81x^4+88x^3+93x^2+95x+13$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22940 885484000 26803159497920 802368664178800000 24013814791080017410700 718709122145939889392896000 21510248621391612523301006523980 643780249376632240926433263652800000 19267699137346231482604127263731989946560 576662967580188447544570545779478078405100000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 129 29585 5176638 895755633 154963936869 26808748368230 4637914180240953 802359176097859393 138808137852176460534 24013807852530545082425

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.aba $\times$ 1.173.at 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.ah_afs $2$ (not in LMFDB) 2.173.h_afs $2$ (not in LMFDB) 2.173.bt_bgi $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ah_afs $2$ (not in LMFDB) 2.173.h_afs $2$ (not in LMFDB) 2.173.bt_bgi $2$ (not in LMFDB) 2.173.ax_qg $4$ (not in LMFDB) 2.173.ap_kk $4$ (not in LMFDB) 2.173.p_kk $4$ (not in LMFDB) 2.173.x_qg $4$ (not in LMFDB)