# Properties

 Label 2.193.abw_bkm 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: $1 - 48 x + 948 x^{2} - 9264 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0177587632772$, $\pm0.239932532337$ Angle rank: $2$ (numerical) Number field: 4.0.2722048.1 Galois group: $D_{4}$ Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=41x^6+10x^5+40x^4+120x^3+37x^2+21x+164$
• $y^2=101x^6+39x^5+100x^4+149x^3+21x^2+119x+32$
• $y^2=99x^6+169x^5+11x^4+45x^3+16x^2+81x+100$
• $y^2=4x^6+149x^5+33x^4+101x^3+190x^2+72x+143$
• $y^2=42x^6+172x^5+79x^4+133x^3+11x^2+163x+178$
• $y^2=21x^6+154x^5+177x^4+6x^3+102x^2+76x+51$
• $y^2=185x^6+54x^5+139x^4+180x^3+112x^2+73x+135$
• $y^2=125x^6+53x^5+150x^4+38x^3+160x^2+4x+123$
• $y^2=100x^6+113x^5+61x^4+62x^3+105x^2+148x+147$
• $y^2=19x^6+35x^5+121x^4+85x^3+16x^2+86x+65$
• $y^2=32x^6+74x^5+25x^4+132x^3+75x^2+143x+93$
• $y^2=136x^6+88x^5+122x^4+13x^3+62x^2+132x+52$
• $y^2=43x^6+73x^5+134x^4+32x^3+44x^2+70x+81$
• $y^2=141x^6+112x^5+20x^4+115x^3+137x^2+39x+66$
• $y^2=129x^6+89x^5+90x^4+121x^3+152x^2+155x+105$
• $y^2=164x^6+131x^5+82x^4+109x^3+37x^2+154x+42$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28886 1372373860 51669078950918 1925124687459859600 71708862828564593649446 2671084435944357955538276260 99495242169023085972128906008502 3706098373864556970033512033996083200 138048458675112028888295571180663169320182 5142167038080440870649076506965438990901547300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 36842 7187186 1387489254 267785027186 51682529681354 9974730034518290 1925122947729218686 371548729845751675538 71708904872657998588682

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.2722048.1.
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_bkm $2$ (not in LMFDB)