# Properties

 Label 2.193.aby_bmt 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: $( 1 - 27 x + 193 x^{2} )( 1 - 23 x + 193 x^{2} )$ Frobenius angles: $\pm0.0758389534121$, $\pm0.189598946136$ Angle rank: $2$ (numerical) Jacobians: 26

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 26 curves, and hence is principally polarizable:

• $y^2=82x^6+11x^5+117x^4+64x^3+45x^2+77x+102$
• $y^2=166x^6+24x^5+186x^4+141x^3+128x^2+138x+57$
• $y^2=83x^6+17x^5+43x^4+99x^3+109x^2+106x+95$
• $y^2=20x^6+151x^5+25x^4+59x^3+130x^2+169x+87$
• $y^2=40x^6+48x^5+165x^4+125x^3+126x^2+7x+22$
• $y^2=37x^6+125x^5+66x^4+62x^3+79x^2+179x+101$
• $y^2=46x^6+88x^5+140x^4+161x^3+32x^2+22x+170$
• $y^2=28x^6+161x^5+154x^4+120x^3+106x^2+92x+6$
• $y^2=41x^6+3x^5+61x^4+69x^3+104x^2+172x+115$
• $y^2=7x^6+115x^5+31x^4+30x^3+78x^2+180x+157$
• $y^2=42x^6+118x^5+44x^4+100x^3+50x^2+31x+43$
• $y^2=162x^6+105x^5+87x^4+50x^3+135x^2+111x+145$
• $y^2=16x^6+129x^5+119x^4+25x^3+137x^2+63x+104$
• $y^2=142x^6+103x^5+80x^4+164x^3+141x^2+44x+70$
• $y^2=20x^6+115x^5+122x^4+17x^3+52x^2+77x+118$
• $y^2=67x^6+138x^5+60x^4+56x^3+58x^2+192x+42$
• $y^2=148x^6+43x^5+129x^4+11x^3+59x^2+7x+5$
• $y^2=102x^6+68x^5+80x^4+23x^3+166x+47$
• $y^2=19x^6+49x^5+34x^4+148x^3+69x^2+175x+22$
• $y^2=13x^6+80x^5+69x^4+68x^3+175x^2+2x+120$
• $y^2=179x^6+172x^5+82x^4+192x^3+156x^2+62x+121$
• $y^2=159x^6+27x^5+111x^4+44x^3+111x^2+27x+159$
• $y^2=84x^6+82x^5+33x^4+121x^3+28x^2+63x+181$
• $y^2=109x^6+152x^5+80x^4+158x^3+10x^2+106x+130$
• $y^2=60x^6+115x^5+112x^4+151x^3+169x^2+152x+182$
• $y^2=13x^6+166x^5+192x^4+187x^3+150x^2+152x+1$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28557 1369508049 51661702001664 1925138074205929401 71709075653424180319557 2671085567746732480095338496 99495246298778054404532289871893 3706098385331371097843764156062122409 138048458699354185953771849657436052468736 5142167038116457419607927719289613476271697249

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36764 7186158 1387498900 267785821944 51682551580478 9974730448540008 1925122953685624804 371548729910997914094 71708904873160259068364

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The isogeny class factors as 1.193.abb $\times$ 1.193.ax 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 $\F_{193}$.

## 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 2.193.ae_ajb $2$ (not in LMFDB) 2.193.e_ajb $2$ (not in LMFDB) 2.193.by_bmt $2$ (not in LMFDB) 2.193.abd_qy $3$ (not in LMFDB) 2.193.ac_ald $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.193.ae_ajb $2$ (not in LMFDB) 2.193.e_ajb $2$ (not in LMFDB) 2.193.by_bmt $2$ (not in LMFDB) 2.193.abd_qy $3$ (not in LMFDB) 2.193.ac_ald $3$ (not in LMFDB) 2.193.aca_bov $6$ (not in LMFDB) 2.193.az_mu $6$ (not in LMFDB) 2.193.c_ald $6$ (not in LMFDB) 2.193.z_mu $6$ (not in LMFDB) 2.193.bd_qy $6$ (not in LMFDB) 2.193.ca_bov $6$ (not in LMFDB)