# Properties

 Label 2.173.abu_bho 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: $1 - 46 x + 872 x^{2} - 7958 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.110664567545$, $\pm0.200287313354$ Angle rank: $2$ (numerical) Number field: 4.0.2772288.1 Galois group: $D_{4}$ Jacobians: 18

This isogeny class is simple and geometrically 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:

• $y^2=68x^6+70x^5+109x^4+54x^3+29x^2+101x+115$
• $y^2=94x^6+44x^5+10x^4+144x^3+17x^2+118x+87$
• $y^2=51x^6+7x^5+123x^4+102x^3+106x^2+57x+123$
• $y^2=7x^6+134x^5+68x^4+51x^3+15x^2+10x+76$
• $y^2=17x^6+69x^5+55x^4+61x^3+82x^2+134x+129$
• $y^2=7x^6+104x^5+9x^4+159x^3+23x^2+70x+79$
• $y^2=59x^6+113x^4+116x^3+56x^2+59x+161$
• $y^2=20x^6+73x^5+52x^4+60x^3+84x^2+79x+46$
• $y^2=47x^6+114x^5+50x^4+77x^3+40x^2+33x+140$
• $y^2=76x^6+141x^5+88x^4+111x^3+163x^2+157x+172$
• $y^2=171x^6+109x^5+141x^4+39x^3+107x^2+151x+150$
• $y^2=90x^6+102x^5+14x^4+55x^3+34x^2+23x+128$
• $y^2=115x^6+23x^5+151x^4+67x^3+128x^2+66x+115$
• $y^2=17x^6+105x^5+108x^4+127x^3+55x^2+4x+3$
• $y^2=8x^6+142x^5+60x^4+72x^3+19x^2+80x+138$
• $y^2=120x^6+43x^5+132x^4+127x^3+93x^2+38x+39$
• $y^2=5x^6+63x^5+24x^4+82x^3+78x^2+163x+138$
• $y^2=53x^6+73x^5+137x^4+49x^3+35x^2+87x+104$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22798 884699188 26804235111838 802393063990308304 24013950198826443390238 718709615709723743121433876 21510249970813891935247398302734 643780252175911282890694904028484608 19267699141312513398931957407016192553182 576662967581705708988630443182184551067533588

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29558 5176844 895782870 154964810668 26808766778774 4637914471195504 802359179586669790 138808137880750303376 24013807852593727958438

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.2772288.1.
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.bu_bho $2$ (not in LMFDB)