# Properties

 Label 2.193.aby_bmw 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: $( 1 - 26 x + 193 x^{2} )( 1 - 24 x + 193 x^{2} )$ Frobenius angles: $\pm0.114714697559$, $\pm0.168091317575$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=41x^6+168x^5+172x^4+82x^3+151x^2+93x+135$
• $y^2=88x^6+98x^5+159x^4+169x^3+44x^2+92x+160$
• $y^2=166x^6+167x^5+71x^4+125x^3+71x^2+167x+166$
• $y^2=97x^6+183x^5+53x^4+32x^3+53x^2+183x+97$
• $y^2=90x^6+90x^5+136x^4+2x^3+136x^2+90x+90$
• $y^2=101x^6+6x^5+12x^4+42x^3+12x^2+6x+101$
• $y^2=116x^6+141x^5+57x^4+188x^3+57x^2+141x+116$
• $y^2=94x^6+93x^5+12x^4+95x^3+144x^2+75x+119$
• $y^2=45x^6+184x^5+119x^4+127x^3+111x^2+28x+17$
• $y^2=151x^6+160x^5+50x^4+89x^3+50x^2+160x+151$
• $y^2=37x^6+176x^5+68x^4+162x^3+68x^2+176x+37$
• $y^2=96x^6+81x^5+83x^4+6x^3+83x^2+81x+96$
• $y^2=155x^5+41x^4+46x^3+41x^2+155x$
• $y^2=79x^6+144x^5+12x^4+11x^3+145x^2+181x+155$
• $y^2=164x^6+106x^5+50x^4+142x^3+138x^2+163x+11$
• $y^2=186x^6+101x^5+160x^4+61x^3+160x^2+101x+186$
• $y^2=13x^6+151x^5+99x^4+117x^3+99x^2+151x+13$
• $y^2=151x^6+125x^5+29x^4+28x^3+29x^2+125x+151$
• $y^2=160x^6+98x^5+53x^4+95x^3+141x^2+83x+182$
• $y^2=177x^6+116x^5+140x^4+148x^3+140x^2+116x+177$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28560 1369737600 51664941553680 1925162909429760000 71709211421119313302800 2671086154826010848925398400 99495248392843040480906060299920 3706098391523911012373494755164160000 138048458713905243850229098043590135505040 5142167038138670382342587055340555582531440000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36770 7186608 1387516798 267786328944 51682562939810 9974730658477008 1925122956902323198 371548729950161169744 71708904873470024818850

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The isogeny class factors as 1.193.aba $\times$ 1.193.ay 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.ac_aje $2$ (not in LMFDB) 2.193.c_aje $2$ (not in LMFDB) 2.193.by_bmw $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.193.ac_aje $2$ (not in LMFDB) 2.193.c_aje $2$ (not in LMFDB) 2.193.by_bmw $2$ (not in LMFDB) 2.193.abo_bcw $4$ (not in LMFDB) 2.193.am_w $4$ (not in LMFDB) 2.193.m_w $4$ (not in LMFDB) 2.193.bo_bcw $4$ (not in LMFDB)