# Properties

 Label 2.173.abu_bhq 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: $( 1 - 24 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$ Frobenius angles: $\pm0.134271185755$, $\pm0.184705758688$ Angle rank: $2$ (numerical) Jacobians: 48

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 48 curves, and hence is principally polarizable:

• $y^2=114x^6+84x^5+137x^4+52x^3+137x^2+84x+114$
• $y^2=113x^6+125x^5+104x^4+155x^3+104x^2+125x+113$
• $y^2=92x^6+85x^5+31x^4+133x^3+31x^2+85x+92$
• $y^2=160x^6+69x^5+101x^4+135x^3+104x^2+3x+122$
• $y^2=67x^6+32x^5+165x^4+68x^3+87x^2+65x+29$
• $y^2=85x^6+123x^5+170x^4+166x^3+170x^2+123x+85$
• $y^2=6x^6+97x^5+37x^4+5x^3+37x^2+97x+6$
• $y^2=x^6+150x^5+73x^4+2x^3+157x^2+163x+149$
• $y^2=87x^6+8x^5+72x^4+47x^3+72x^2+8x+87$
• $y^2=3x^6+58x^5+30x^4+66x^3+30x^2+58x+3$
• $y^2=106x^6+140x^5+52x^4+89x^3+121x^2+140x+67$
• $y^2=125x^6+139x^5+136x^4+112x^3+25x^2+148x+42$
• $y^2=53x^6+71x^5+90x^4+160x^3+96x^2+110x+155$
• $y^2=9x^6+43x^5+105x^4+113x^3+62x^2+164x+132$
• $y^2=71x^6+92x^5+79x^4+148x^3+79x^2+92x+71$
• $y^2=59x^6+153x^5+49x^4+49x^2+153x+59$
• $y^2=55x^6+31x^5+154x^4+162x^3+154x^2+31x+55$
• $y^2=80x^6+35x^5+57x^4+43x^3+78x^2+78x+123$
• $y^2=109x^6+79x^5+16x^4+132x^3+6x^2+3x+148$
• $y^2=154x^6+99x^5+87x^4+63x^3+154x^2+58x+70$
• and 28 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22800 884822400 26805666358800 802401972083712000 24013988905912734234000 718709744388026762386646400 21510250302529775421369242278800 643780252784264583416961360052224000 19267699141701010546026872886127142672400 576662967579049165478832439672975291934832000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29562 5177120 895792814 154965060448 26808771578634 4637914542718144 802359180344875486 138808137883549110080 24013807852483102291482

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ay $\times$ 1.173.aw 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.ac_aha $2$ (not in LMFDB) 2.173.c_aha $2$ (not in LMFDB) 2.173.bu_bhq $2$ (not in LMFDB)