# Properties

 Label 2.173.abw_bjm 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: $( 1 - 24 x + 173 x^{2} )^{2}$ Frobenius angles: $\pm0.134271185755$, $\pm0.134271185755$ Angle rank: $1$ (numerical) Jacobians: 39

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 39 curves, and hence is principally polarizable:

• $y^2=165x^6+139x^5+136x^4+151x^3+14x^2+6x+63$
• $y^2=71x^6+76x^5+78x^4+27x^3+78x^2+76x+71$
• $y^2=129x^6+103x^5+59x^4+142x^3+2x^2+146x+42$
• $y^2=8x^6+145x^5+29x^4+63x^3+119x^2+115x+68$
• $y^2=150x^6+100x^5+62x^4+95x^3+153x^2+133x+64$
• $y^2=98x^6+149x^5+134x^4+99x^3+2x^2+118x+143$
• $y^2=59x^6+86x^5+160x^4+121x^3+100x^2+39x+108$
• $y^2=33x^6+170x^5+26x^4+49x^3+21x^2+152x+137$
• $y^2=92x^6+14x^5+120x^4+8x^3+161x^2+142x+139$
• $y^2=38x^6+x^5+43x^4+120x^3+43x^2+x+38$
• $y^2=44x^6+122x^5+50x^4+46x^3+93x^2+167x+8$
• $y^2=65x^6+93x^5+94x^4+10x^3+32x^2+166x+105$
• $y^2=170x^6+31x^4+31x^2+170$
• $y^2=96x^6+132x^5+12x^4+60x^3+12x^2+132x+96$
• $y^2=170x^6+18x^5+120x^4+86x^3+125x^2+79x+86$
• $y^2=103x^6+4x^5+47x^4+111x^3+47x^2+4x+103$
• $y^2=167x^6+56x^5+39x^4+64x^3+79x^2+172x+14$
• $y^2=84x^6+90x^5+87x^4+67x^3+26x^2+122x+16$
• $y^2=92x^6+158x^5+3x^4+49x^3+3x^2+158x+92$
• $y^2=101x^6+94x^5+66x^4+35x^3+26x^2+91x+5$
• and 19 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22500 882090000 26794599322500 802371645504000000 24013932957293468062500 718709710112381370219210000 21510250540458302770593295522500 643780254081975313572514612224000000 19267699145892077385283975716465781222500 576662967589178786731288173916267438982250000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 126 29470 5174982 895758958 154964699406 26808770300110 4637914594018902 802359181962244318 138808137913742345886 24013807852904927156350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-29})$$$)$
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_aiw $2$ (not in LMFDB) 2.173.bw_bjm $2$ (not in LMFDB) 2.173.y_pn $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.a_aiw $2$ (not in LMFDB) 2.173.bw_bjm $2$ (not in LMFDB) 2.173.y_pn $3$ (not in LMFDB) 2.173.a_iw $4$ (not in LMFDB) 2.173.ay_pn $6$ (not in LMFDB)