# Properties

 Label 2.173.abu_bhr 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: $( 1 - 23 x + 173 x^{2} )^{2}$ Frobenius angles: $\pm0.161302001611$, $\pm0.161302001611$ Angle rank: $1$ (numerical) Jacobians: 7

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 7 curves, and hence is principally polarizable:

• $y^2=144x^6+65x^5+123x^4+7x^3+69x^2+75x+138$
• $y^2=116x^6+60x^5+24x^4+80x^3+166x^2+126x+69$
• $y^2=89x^6+68x^5+76x^4+38x^3+138x^2+36x+73$
• $y^2=17x^6+25x^5+70x^4+119x^3+91x^2+79x+85$
• $y^2=10x^6+124x^5+129x^4+168x^3+37x^2+94x+21$
• $y^2=36x^6+149x^5+20x^4+118x^3+123x^2+65x+66$
• $y^2=9x^6+56x^5+112x^4+40x^3+26x^2+160x+118$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22801 884884009 26806381990144 802406420764930921 24014008152537131333641 718709807617138222971621376 21510250460394996583407142930081 643780253043866322366654638191305609 19267699141692080490441191421122782279936 576662967576944433891806754651600326709227449

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29564 5177258 895797780 154965184648 26808773937158 4637914576756120 802359180668423524 138808137883484776274 24013807852395455567564

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-163})$$$)$
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.a_ahb $2$ (not in LMFDB) 2.173.bu_bhr $2$ (not in LMFDB) 2.173.x_ns $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.a_ahb $2$ (not in LMFDB) 2.173.bu_bhr $2$ (not in LMFDB) 2.173.x_ns $3$ (not in LMFDB) 2.173.a_hb $4$ (not in LMFDB) 2.173.ax_ns $6$ (not in LMFDB)