# Properties

 Label 2.191.abz_bno 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: $1 - 51 x + 1028 x^{2} - 9741 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0240713736749$, $\pm0.177822725834$ Angle rank: $2$ (numerical) Number field: 4.0.270504.1 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:

• $y^2=101x^6+19x^5+155x^4+157x^3+180x^2+176x+178$
• $y^2=91x^6+146x^5+181x^4+163x^3+56x^2+134x+129$
• $y^2=154x^6+113x^5+33x^4+151x^3+38x^2+2x+33$
• $y^2=84x^6+2x^5+172x^4+190x^3+39x^2+173x+50$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27718 1311116836 48519254825752 1771164416850588576 64615050886962155727298 2357221626132998760043215424 85993799931149352921344523081922 3137139821959443459332799921150885504 114445997931413107046476929390998695144312 4175104450980470191127129159624398411299113476

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 141 35937 6963282 1330838665 254194912611 48551227375722 9273284190248373 1771197284103921649 338298681519571728942 64615048177118774421177

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.270504.1.
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.bz_bno $2$ (not in LMFDB)