# Properties

 Label 2.191.abz_bnp 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: $1 - 51 x + 1029 x^{2} - 9741 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0498136467200$, $\pm0.172118248730$ Angle rank: $2$ (numerical) Number field: 4.0.634933.1 Galois group: $C_4$ 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:

• $y^2=25x^6+79x^5+65x^4+135x^3+178x^2+29x+20$
• $y^2=185x^6+32x^5+56x^4+122x^3+2x^2+105x+109$
• $y^2=145x^6+149x^5+47x^4+110x^3+14x^2+76x+62$
• $y^2=148x^6+181x^5+98x^4+130x^3+40x^2+118x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27719 1311191857 48520322483789 1771172788704310813 64615098529676835926384 2357221845991117542368665513 85993800800661972880824456866081 3137139825001429940664072326564248053 114445997941023473548179175988619731910851 4175104451008334786712855060698950315502924032

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 141 35939 6963435 1330844955 254195100036 48551231904095 9273284284013709 1771197285821396323 338298681547979662599 64615048177550014455374

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.634933.1.
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_bnp $2$ (not in LMFDB)