# Properties

 Label 2.193.abw_bla 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: $( 1 - 24 x + 193 x^{2} )^{2}$ Frobenius angles: $\pm0.168091317575$, $\pm0.168091317575$ Angle rank: $1$ (numerical) Jacobians: 34

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 34 curves, and hence is principally polarizable:

• $y^2=76x^6+161x^5+28x^4+118x^3+28x^2+161x+76$
• $y^2=139x^6+191x^5+137x^4+79x^3+75x^2+31x+6$
• $y^2=27x^6+126x^5+148x^4+16x^3+67x^2+54x+26$
• $y^2=158x^6+108x^5+67x^4+56x^3+23x^2+85x+133$
• $y^2=172x^6+99x^5+160x^4+191x^3+174x^2+103x+137$
• $y^2=180x^6+46x^5+43x^4+88x^3+90x^2+148x+152$
• $y^2=123x^6+172x^5+149x^4+40x^3+61x^2+4x+40$
• $y^2=182x^6+6x^5+2x^4+125x^3+100x^2+24x+157$
• $y^2=187x^6+100x^5+112x^4+44x^3+89x^2+134x+109$
• $y^2=15x^5+143x^4+135x^3+98x^2+141x$
• $y^2=72x^6+84x^5+190x^4+96x^3+98x^2+190x$
• $y^2=91x^6+144x^5+68x^4+38x^3+106x^2+3x+82$
• $y^2=149x^6+97x^5+59x^4+82x^3+101x^2+191x+141$
• $y^2=129x^6+121x^5+86x^4+48x^3+48x^2+126x+67$
• $y^2=26x^6+90x^5+102x^4+102x^2+90x+26$
• $y^2=68x^6+165x^5+106x^4+31x^3+174x^2+81x+35$
• $y^2=64x^6+169x^5+30x^4+12x^3+30x^2+169x+64$
• $y^2=36x^6+82x^5+57x^4+168x^3+119x^2+164x+127$
• $y^2=7x^6+154x^5+72x^4+156x^3+145x^2+47x+98$
• $y^2=127x^6+100x^5+67x^4+116x^3+64x^2+115x+29$
• and 14 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28900 1373443600 51683590156900 1925229510696960000 71709390988296636422500 2671086483284152145855952400 99495248463399037299797226172900 3706098388862990664067605070479360000 138048458699079064512721462633179600316900 5142167038083624773322742904199738441034090000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 36870 7189202 1387564798 267786999506 51682569295110 9974730665550482 1925122955520115198 371548729910257442066 71708904872702398969350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The isogeny class factors as 1.193.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$
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.a_ahi $2$ (not in LMFDB) 2.193.bw_bla $2$ (not in LMFDB) 2.193.y_ot $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.193.a_ahi $2$ (not in LMFDB) 2.193.bw_bla $2$ (not in LMFDB) 2.193.y_ot $3$ (not in LMFDB) 2.193.abm_bbu $4$ (not in LMFDB) 2.193.abc_wk $4$ (not in LMFDB) 2.193.ak_by $4$ (not in LMFDB) 2.193.a_hi $4$ (not in LMFDB) 2.193.k_by $4$ (not in LMFDB) 2.193.bc_wk $4$ (not in LMFDB) 2.193.bm_bbu $4$ (not in LMFDB) 2.193.ay_ot $6$ (not in LMFDB) 2.193.a_amy $8$ (not in LMFDB) 2.193.a_my $8$ (not in LMFDB) 2.193.ao_d $12$ (not in LMFDB) 2.193.o_d $12$ (not in LMFDB)