# Properties

 Label 2.191.abw_bkn Base Field $\F_{191}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{191}$ Dimension: $2$ L-polynomial: $( 1 - 27 x + 191 x^{2} )( 1 - 21 x + 191 x^{2} )$ Frobenius angles: $\pm0.0686610702072$, $\pm0.225319681555$ Angle rank: $2$ (numerical) Jacobians: 56

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 56 curves, and hence is principally polarizable:

• $y^2=28x^6+190x^5+144x^4+68x^3+48x^2+106x+93$
• $y^2=11x^6+151x^5+26x^4+4x^3+175x^2+74x+119$
• $y^2=65x^6+108x^5+177x^4+49x^3+32x^2+163x+33$
• $y^2=16x^6+138x^5+110x^4+3x^3+111x^2+43x+92$
• $y^2=181x^6+60x^5+143x^4+15x^3+186x^2+143x+163$
• $y^2=115x^6+129x^5+181x^4+5x^3+112x^2+33x+27$
• $y^2=63x^6+123x^5+105x^4+96x^3+109x^2+49x+86$
• $y^2=76x^6+163x^5+11x^4+35x^3+66x^2+15x+155$
• $y^2=9x^6+171x^5+183x^4+154x^3+185x^2+132x+156$
• $y^2=105x^6+65x^5+23x^4+11x^3+176x^2+122x+118$
• $y^2=23x^6+175x^5+120x^4+44x^3+161x^2+45x+182$
• $y^2=131x^6+13x^5+153x^4+113x^3+6x^2+49x+62$
• $y^2=73x^6+65x^5+144x^4+47x^3+102x^2+43x+47$
• $y^2=164x^6+160x^5+144x^4+63x^3+92x^2+4x+70$
• $y^2=178x^6+58x^5+37x^4+3x^3+33x^2+129x+67$
• $y^2=169x^6+162x^5+139x^4+98x^3+182x^2+170x+36$
• $y^2=135x^6+104x^5+92x^4+96x^3+25x^2+113x+69$
• $y^2=167x^6+85x^5+154x^4+171x^3+179x^2+174x+23$
• $y^2=28x^6+6x^5+156x^4+165x^3+117x^2+75x+167$
• $y^2=162x^6+174x^5+147x^4+91x^3+61x^2+64x+14$
• and 36 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28215 1316145105 48541194797040 1771226609260596345 64615163346536461275375 2357221691360552948005536000 85993799651427907735931749462335 3137139821592665603258026237554590505 114445997937055231688557018298209488597360 4175104451024740279854947565026894669016782625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36076 6966432 1330885396 254195355024 48551228719198 9273284160084144 1771197283896842596 338298681536249667552 64615048177803910314076

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.abb $\times$ 1.191.av 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 $\F_{191}$.

## 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 2.191.ag_ahd $2$ (not in LMFDB) 2.191.g_ahd $2$ (not in LMFDB) 2.191.bw_bkn $2$ (not in LMFDB)