# Properties

 Label 2.191.aca_boq 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: $1 - 52 x + 1056 x^{2} - 9932 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0407629633776$, $\pm0.151065030898$ Angle rank: $2$ (numerical) Number field: 4.0.127232.1 Galois group: $D_{4}$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=128x^6+128x^5+69x^4+122x^3+171x^2+68x+151$
• $y^2=63x^6+43x^4+187x^3+26x^2+189x+76$
• $y^2=49x^6+77x^5+142x^4+187x^3+80x^2+60x+190$
• $y^2=21x^6+8x^5+74x^4+104x^3+46x^2+54x+141$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27554 1309421188 48511750095746 1771143887259580688 64615026883385448761794 2357221733620401461778092548 85993800830980474943173177986914 3137139825990975068538543245031391232 114445997945204380090285217468755161476834 4175104451019061812564125558087986967299701508

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 140 35890 6962204 1330823238 254194818180 48551229589618 9273284287283156 1771197286380083454 338298681560338287596 64615048177716028815090

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.127232.1.
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.ca_boq $2$ (not in LMFDB)