# Properties

 Label 2.191.abx_bln 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: $1 - 49 x + 975 x^{2} - 9359 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0573856553654$, $\pm0.210617421473$ Angle rank: $2$ (numerical) Number field: 4.0.5958485.4 Galois group: $D_{4}$ Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=86x^6+108x^5+76x^4+132x^3+150x^2+5x+28$
• $y^2=142x^6+140x^5+22x^4+110x^3+89x^2+176$
• $y^2=79x^6+189x^5+118x^4+42x^3+151x^2+49x+37$
• $y^2=139x^6+14x^5+141x^4+170x^3+167x^2+62x+31$
• $y^2=176x^6+136x^5+13x^4+157x^3+44x^2+129x+45$
• $y^2=131x^6+3x^5+41x^4+41x^3+x^2+175x+172$
• $y^2=102x^6+166x^5+37x^4+144x^3+87x^2+68x+160$
• $y^2=179x^6+101x^5+74x^4+34x^3+109x^2+114x+187$
• $y^2=26x^6+x^5+96x^4+188x^3+86x^2+123x+121$
• $y^2=78x^6+142x^5+155x^4+171x^3+21x^2+55x+47$
• $y^2=145x^6+156x^5+117x^4+142x^3+122x^2+150x+161$
• $y^2=76x^6+8x^5+177x^4+94x^3+41x^2+52x+71$
• $y^2=146x^6+174x^5+129x^4+57x^3+118x^2+84x+22$
• $y^2=127x^6+84x^5+64x^4+47x^3+143x^2+93x+7$
• $y^2=30x^6+89x^5+161x^4+66x^3+126x^2+187x+89$
• $y^2=29x^6+156x^5+49x^4+146x^3+116x^2+80x+14$
• $y^2=85x^6+165x^5+47x^4+184x^3+57x^2+58x+177$
• $y^2=75x^6+19x^5+113x^4+30x^3+82x^2+126x+153$
• $y^2=123x^6+65x^5+33x^4+57x^3+180x^2+125x+41$
• $y^2=127x^6+126x^5+125x^4+33x^3+96x^2+42x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28049 1314516385 48534500731031 1771209806888796365 64615141893324404297104 2357221712080479134960148625 85993799790282623778366500911259 3137139821509877036166511533358544885 114445997933808573872913313896271651283381 4175104451006074838465713572981551345501344000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 143 36031 6965471 1330872771 254195270628 48551229145963 9273284175057773 1771197283850101011 338298681526652651681 64615048177515038883726

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.5958485.4.
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.bx_bln $2$ (not in LMFDB)