# Properties

 Label 2.193.abw_bku Base Field $\F_{193}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{193}$ Dimension: $2$ L-polynomial: $1 - 48 x + 956 x^{2} - 9264 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0990880211071$, $\pm0.217437428422$ Angle rank: $2$ (numerical) Number field: 4.0.12830976.1 Galois group: $D_{4}$ Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=21x^6+11x^5+22x^4+80x^3+71x^2+29x+39$
• $y^2=70x^6+32x^5+45x^4+154x^3+160x^2+183x+124$
• $y^2=17x^6+112x^5+15x^4+44x^3+79x^2+33x+66$
• $y^2=82x^6+76x^5+53x^4+121x^3+108x^2+181x+61$
• $y^2=115x^6+150x^5+167x^4+15x^3+97x^2+149x+159$
• $y^2=96x^6+101x^5+110x^4+166x^3+27x^2+80x+83$
• $y^2=114x^6+146x^5+153x^4+11x^3+165x^2+65x+73$
• $y^2=46x^6+161x^5+57x^4+121x^3+117x^2+51x+48$
• $y^2=101x^6+40x^5+137x^4+171x^3+110x^2+101x+97$
• $y^2=33x^6+135x^5+46x^4+42x^3+109x^2+52x+184$
• $y^2=179x^6+2x^5+162x^4+93x^3+43x^2+129x+66$
• $y^2=60x^6+170x^5+58x^4+126x^3+120x^2+177x+186$
• $y^2=118x^6+72x^5+167x^4+20x^3+118x^2+159x+52$
• $y^2=133x^6+162x^5+93x^4+80x^3+20x^2+157x+33$
• $y^2=93x^6+44x^5+48x^4+26x^3+171x^2+168x+167$
• $y^2=96x^6+97x^5+130x^4+31x^3+12x^2+156x+81$
• $y^2=27x^6+66x^5+31x^4+39x^3+13x^2+126x+103$
• $y^2=37x^6+26x^5+39x^4+171x^3+111x^2+129x+26$
• $y^2=189x^6+141x^5+55x^4+137x^3+105x^2+192x+65$
• $y^2=5x^6+184x^5+112x^4+64x^3+187x^2+145x+160$
• $y^2=3x^6+171x^5+52x^4+78x^3+190x^2+82x+152$
• $y^2=33x^6+85x^5+146x^4+39x^3+74x^2+28x+141$
• $y^2=128x^6+102x^5+69x^4+98x^3+84x^2+136x+167$
• $y^2=61x^6+119x^5+35x^4+49x^3+92x^2+77x+172$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28894 1372985092 51677370931054 1925184719481016464 71709167718882851495374 2671085643074096602959820996 99495246077097509472069346395262 3706098384453445341660191495197593600 138048458699543876894729900888626122466366 5142167038130571923099034900005008448210442052

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 36858 7188338 1387532518 267786165746 51682553037978 9974730426315794 1925122953229588606 371548729911508455314 71708904873357089622618

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.12830976.1.
All geometric endomorphisms are defined over $\F_{193}$.

## 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 2.193.bw_bku $2$ (not in LMFDB)