Properties

 Label 2.173.abt_bgo 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: $( 1 - 25 x + 173 x^{2} )( 1 - 20 x + 173 x^{2} )$ Frobenius angles: $\pm0.100717649571$, $\pm0.225058830207$ 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:

• $y^2=75x^6+126x^5+154x^4+40x^3+93x^2+90x+28$
• $y^2=27x^6+7x^5+53x^4+30x^3+139x^2+53x+141$
• $y^2=144x^6+145x^4+78x^3+161x^2+82x+162$
• $y^2=69x^6+53x^5+52x^4+131x^3+83x^2+110x+79$
• $y^2=172x^6+154x^5+145x^4+69x^3+30x^2+83x+103$
• $y^2=17x^6+57x^5+114x^4+104x^3+88x^2+159x+69$
• $y^2=90x^6+18x^5+116x^4+130x^3+109x^2+103x+93$
• $y^2=136x^6+41x^5+69x^4+156x^3+69x^2+68x+81$
• $y^2=45x^6+24x^5+165x^4+28x^3+153x^2+158x+107$
• $y^2=133x^6+4x^5+96x^4+69x^3+103x^2+171x+86$
• $y^2=104x^6+33x^5+104x^4+98x^3+151x^2+88x+131$
• $y^2=76x^6+63x^5+72x^4+147x^3+103x^2+148x+24$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22946 885853276 26807359396664 802394076574685056 24013921902477812598986 718709470333441169314014976 21510249530565660366886889391194 643780251298629731216236286312640000 19267699140573936841347359972443508920376 576662967584306941206781120088883579780214396

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 129 29597 5177448 895784001 154964628069 26808761356058 4637914376271753 802359178493292193 138808137875429458584 24013807852702050313397

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.az $\times$ 1.173.au 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.af_afy $2$ (not in LMFDB) 2.173.f_afy $2$ (not in LMFDB) 2.173.bt_bgo $2$ (not in LMFDB)