# Properties

 Label 2.173.abu_bhi 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: $( 1 - 26 x + 173 x^{2} )( 1 - 20 x + 173 x^{2} )$ Frobenius angles: $\pm0.0485897903475$, $\pm0.225058830207$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=168x^6+54x^5+120x^4+108x^3+25x^2+19x+166$
• $y^2=97x^6+60x^5+69x^4+107x^3+38x^2+61x+76$
• $y^2=131x^6+15x^5+68x^4+46x^3+68x^2+15x+131$
• $y^2=99x^6+153x^5+139x^4+15x^3+118x^2+56x+41$
• $y^2=102x^6+22x^5+70x^4+7x^3+70x^2+22x+102$
• $y^2=6x^6+136x^5+134x^4+69x^3+110x^2+163x+169$
• $y^2=82x^6+99x^5+120x^4+58x^3+14x^2+68x+108$
• $y^2=116x^6+103x^5+90x^4+58x^3+135x^2+40x+80$
• $y^2=x^6+78x^5+124x^4+48x^3+47x^2+148x+16$
• $y^2=127x^6+31x^5+118x^4+126x^3+80x^2+29x+98$
• $y^2=131x^6+9x^5+14x^4+61x^3+121x^2+124x+142$
• $y^2=6x^6+22x^5+106x^4+83x^3+107x^2+102x+93$
• $y^2=42x^6+82x^5+120x^4+63x^3+70x^2+32x+128$
• $y^2=66x^6+15x^5+68x^4+88x^2+59x+152$
• $y^2=99x^6+142x^5+94x^4+69x^3+25x^2+81x+77$
• $y^2=110x^6+66x^5+116x^4+9x^3+55x^2+78x+19$
• $y^2=44x^6+122x^5+165x^4+97x^3+114x^2+31x+113$
• $y^2=124x^6+153x^5+111x^4+49x^3+51x^2+83x+142$
• $y^2=29x^6+157x^5+24x^4+74x^3+49x^2+55x+142$
• $y^2=104x^6+126x^5+171x^4+76x^3+118x^2+34x+96$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22792 884329600 26799941496328 802366253860864000 24013832366865170070472 718709211891008664601475200 21510248847137557929528484527688 643780249628334982866154613145600000 19267699136803332855078348111026017545352 576662967576536666818134472099765715706448000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29546 5176016 895752942 154964050288 26808751715834 4637914228914976 802359176411562718 138808137848265316448 24013807852378475042186

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.aba $\times$ 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ag_ags $2$ (not in LMFDB) 2.173.g_ags $2$ (not in LMFDB) 2.173.bu_bhi $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ag_ags $2$ (not in LMFDB) 2.173.g_ags $2$ (not in LMFDB) 2.173.bu_bhi $2$ (not in LMFDB) 2.173.ay_qk $4$ (not in LMFDB) 2.173.aq_kg $4$ (not in LMFDB) 2.173.q_kg $4$ (not in LMFDB) 2.173.y_qk $4$ (not in LMFDB)