# Properties

 Label 2.191.abw_bkw Base Field $\F_{191}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{191}$ Dimension: $2$ L-polynomial: $( 1 - 24 x + 191 x^{2} )^{2}$ Frobenius angles: $\pm0.165219579186$, $\pm0.165219579186$ Angle rank: $1$ (numerical) Jacobians: 105

This isogeny class is not 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 105 curves, and hence is principally polarizable:

• $y^2=57x^6+158x^5+177x^4+87x^3+72x^2+51x+76$
• $y^2=28x^6+47x^5+8x^4+106x^3+8x^2+47x+28$
• $y^2=24x^6+183x^5+179x^4+149x^3+173x^2+173x+81$
• $y^2=186x^6+180x^5+173x^4+28x^3+38x^2+17x+57$
• $y^2=61x^6+38x^4+38x^2+61$
• $y^2=55x^6+31x^5+132x^4+107x^3+162x^2+168$
• $y^2=41x^6+164x^5+35x^4+8x^3+38x^2+123x+178$
• $y^2=14x^6+87x^5+70x^4+109x^3+70x^2+87x+14$
• $y^2=189x^6+61x^5+113x^4+108x^3+71x^2+89x+88$
• $y^2=24x^6+39x^5+113x^4+47x^3+94x^2+135x+144$
• $y^2=26x^6+64x^5+180x^4+179x^3+177x^2+50x+15$
• $y^2=150x^6+94x^5+26x^4+180x^3+26x^2+94x+150$
• $y^2=114x^6+110x^5+3x^4+144x^3+3x^2+110x+114$
• $y^2=7x^6+68x^5+49x^4+165x^3+49x^2+68x+7$
• $y^2=111x^6+77x^5+65x^4+180x^3+65x^2+77x+111$
• $y^2=132x^6+43x^5+17x^4+68x^3+149x^2+10x+152$
• $y^2=190x^6+93x^5+186x^4+33x^3+73x^2+21x+76$
• $y^2=94x^6+80x^5+130x^4+36x^3+169x^2+131x+67$
• $y^2=125x^6+146x^5+87x^4+25x^3+87x^2+146x+125$
• $y^2=163x^6+148x^4+148x^2+163$
• and 85 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28224 1316818944 48550236840000 1771291317720121344 64615486195582895006784 2357222925268823977290240000 85993803337883348580090475788864 3137139829710017809760575045657165824 114445997945963658832753447197055217640000 4175104450999330185526910143441559679133814784

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36094 6967728 1330934014 254196625104 48551254133758 9273284557619184 1771197288479817214 338298681562582691088 64615048177410656806654

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-47})$$$)$
All geometric endomorphisms are defined over $\F_{191}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.191.a_ahm $2$ (not in LMFDB) 2.191.bw_bkw $2$ (not in LMFDB) 2.191.y_ov $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.191.a_ahm $2$ (not in LMFDB) 2.191.bw_bkw $2$ (not in LMFDB) 2.191.y_ov $3$ (not in LMFDB) 2.191.a_hm $4$ (not in LMFDB) 2.191.ay_ov $6$ (not in LMFDB)