# Properties

 Label 2.173.abt_bgs 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: $( 1 - 24 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$ Frobenius angles: $\pm0.134271185755$, $\pm0.205732831898$ Angle rank: $2$ (numerical) Jacobians: 42

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 42 curves, and hence is principally polarizable:

• $y^2=136x^6+127x^5+60x^4+55x^3+125x^2+153x+170$
• $y^2=110x^6+91x^5+102x^4+106x^3+167x^2+33x+21$
• $y^2=107x^6+141x^5+117x^4+16x^3+166x+45$
• $y^2=80x^6+34x^5+97x^4+73x^3+164x^2+107x+6$
• $y^2=86x^6+75x^5+45x^4+101x^3+108x^2+123x+167$
• $y^2=36x^5+55x^4+5x^3+154x^2+64x+45$
• $y^2=98x^6+60x^5+69x^4+94x^3+155x^2+79x+70$
• $y^2=18x^6+158x^5+77x^4+161x^3+166x^2+82x+67$
• $y^2=134x^6+68x^5+29x^4+2x^3+152x^2+81x+44$
• $y^2=32x^6+7x^5+155x^4+70x^3+34x^2+74x+111$
• $y^2=9x^6+101x^5+33x^4+56x^3+152x^2+64x+22$
• $y^2=158x^6+18x^5+13x^4+157x^3+74x^2+90x+131$
• $y^2=17x^6+77x^5+41x^4+100x^3+154x^2+60x$
• $y^2=146x^6+74x^5+27x^4+135x^3+79x^2+96x+103$
• $y^2=70x^6+133x^5+74x^4+69x^3+126x^2+98x+14$
• $y^2=8x^6+146x^5+x^4+113x^3+101x^2+170x+84$
• $y^2=146x^6+13x^5+5x^4+119x^3+91x^2+73x+141$
• $y^2=27x^6+132x^5+64x^4+63x^3+116x^2+79x+140$
• $y^2=93x^6+x^5+123x^4+156x^3+165x^2+124x+161$
• $y^2=76x^6+34x^5+106x^4+57x^3+37x^2+82x+28$
• and 22 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22950 886099500 26810159430600 802410946623000000 24013991915474321994750 718709688353854105036128000 21510250038097269046508213085150 643780252047529323097499087388000000 19267699140376158772989253203739140385800 576662967578326840345522412071609257111487500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 129 29605 5177988 895802833 154965079869 26808769488490 4637914485702753 802359179426664193 138808137874004628084 24013807852453022716525

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ay $\times$ 1.173.av 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.ad_agc $2$ (not in LMFDB) 2.173.d_agc $2$ (not in LMFDB) 2.173.bt_bgs $2$ (not in LMFDB)