# Properties

 Label 2.191.abv_bjj 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: $1 - 47 x + 919 x^{2} - 8977 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0415744860853$, $\pm0.249183751291$ Angle rank: $2$ (numerical) Number field: 4.0.733037.1 Galois group: $D_{4}$ Jacobians: 25

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 25 curves, and hence is principally polarizable:

• $y^2=91x^6+42x^5+155x^4+171x^3+147x^2+77x+182$
• $y^2=89x^6+118x^5+88x^4+162x^3+181x^2+161x+23$
• $y^2=120x^6+19x^5+158x^4+30x^3+176x^2+175x+146$
• $y^2=55x^6+81x^5+129x^4+151x^3+65x^2+155x+128$
• $y^2=96x^6+182x^5+26x^4+12x^3+77x^2+132x+156$
• $y^2=146x^6+142x^5+177x^4+37x^3+147x^2+77x+116$
• $y^2=175x^6+130x^5+153x^4+122x^3+111x^2+189x+181$
• $y^2=116x^6+19x^5+107x^4+3x^3+39x^2+138x+61$
• $y^2=69x^6+4x^5+47x^4+182x^3+83x^2+158x+133$
• $y^2=142x^6+177x^5+180x^4+187x^3+160x^2+45x+112$
• $y^2=50x^6+45x^5+92x^4+186x^3+5x^2+82x+189$
• $y^2=179x^6+77x^5+16x^4+51x^3+105x^2+186x+105$
• $y^2=19x^6+181x^5+121x^4+130x^3+96x^2+49x+109$
• $y^2=145x^6+95x^5+146x^4+149x^3+174x^2+134x+14$
• $y^2=186x^6+127x^5+91x^4+135x^3+82x^2+158x+7$
• $y^2=31x^6+153x^5+43x^4+45x^3+16x^2+28x+36$
• $y^2=66x^6+36x^5+178x^4+47x^3+117x^2+16x+180$
• $y^2=81x^6+176x^5+40x^4+100x^3+164x^2+27x+106$
• $y^2=55x^6+62x^5+182x^4+82x^3+49x^2+33x+126$
• $y^2=38x^6+86x^5+98x^4+61x^3+187x^2+83x+175$
• $y^2=22x^6+29x^5+54x^4+58x^3+103x^2+55x+173$
• $y^2=168x^6+56x^5+148x^4+15x^3+74x^2+159x+172$
• $y^2=18x^6+78x^5+117x^4+189x^3+150x^2+28x+34$
• $y^2=83x^6+70x^5+139x^4+102x^3+153x^2+113x+146$
• $y^2=171x^6+57x^5+159x^4+125x^3+178x^2+44x+166$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28377 1317402225 48543034884975 1771210231670508525 64615028154367770644112 2357221103729789406710270625 85993797859055009289398614294467 3137139817621653505676007301365964725 114445997931152929157483854606656556344525 4175104451020123887825978043047648861102240000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 145 36111 6966697 1330873091 254194823180 48551216615883 9273283966800635 1771197281654849491 338298681518802651487 64615048177732465779726

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.733037.1.
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.bv_bjj $2$ (not in LMFDB)