# Properties

 Label 2.191.abv_bjo 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: $1 - 47 x + 924 x^{2} - 8977 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0832068261027$, $\pm0.237476928001$ Angle rank: $2$ (numerical) Number field: 4.0.30190760.1 Galois group: $D_{4}$ Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=161x^6+185x^5+36x^4+149x^3+183x^2+55x+118$
• $y^2=76x^6+8x^5+13x^4+64x^3+97x^2+49x+42$
• $y^2=38x^6+172x^5+83x^4+54x^3+82x^2+109x+153$
• $y^2=165x^6+122x^5+23x^4+61x^3+4x^2+83x+156$
• $y^2=19x^6+100x^5+34x^4+162x^3+177x^2+68x+3$
• $y^2=159x^6+134x^5+179x^4+167x^3+6x^2+87x+148$
• $y^2=113x^6+120x^5+50x^4+129x^3+178x^2+64x+16$
• $y^2=76x^6+70x^5+154x^4+90x^3+91x^2+179x+16$
• $y^2=44x^6+142x^5+35x^4+64x^3+129x^2+73x+126$
• $y^2=58x^6+132x^5+54x^4+25x^3+183x^2+153x+160$
• $y^2=106x^6+80x^5+122x^4+81x^3+121x^2+78x+26$
• $y^2=177x^6+148x^5+26x^4+108x^3+159x^2+137x+39$
• $y^2=114x^6+163x^5+168x^4+145x^3+3x^2+175x+91$
• $y^2=186x^6+85x^5+143x^4+135x^3+127x^2+7x+186$
• $y^2=142x^6+106x^5+133x^4+165x^3+131x^2+51x+99$
• $y^2=189x^6+156x^5+151x^4+36x^3+72x^2+5x+154$
• $y^2=34x^6+8x^5+43x^4+110x^3+29x^2+67x+8$
• $y^2=128x^6+5x^5+171x^4+25x^3+14x^2+50x+149$
• $y^2=181x^6+186x^5+123x^4+45x^3+130x^2+45x+152$
• $y^2=127x^6+25x^5+64x^4+84x^3+75x^2+137x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28382 1317776260 48547953096200 1771244503379092640 64615194518934045052762 2357221729198489312223656000 85993799774752205851157765284922 3137139822563150866135261937902828160 114445997942408848862190322656041772405800 4175104451045350237844073213676004174177486500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 145 36121 6967402 1330898841 254195477655 48551229498538 9273284173383025 1771197284444768721 338298681552074787382 64615048178122875610401

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.30190760.1.
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_bjo $2$ (not in LMFDB)