# Properties

 Label 2.191.abw_bkv 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: $( 1 - 25 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$ Frobenius angles: $\pm0.140267993779$, $\pm0.187132320568$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=42x^6+132x^5+43x^4+162x^3+75x^2+55x+166$
• $y^2=114x^6+41x^5+40x^4+169x^3+25x^2+19x+139$
• $y^2=57x^6+95x^5+177x^4+138x^3+18x^2+44x+37$
• $y^2=118x^6+60x^5+24x^4+122x^3+136x^2+144x+115$
• $y^2=61x^6+52x^5+133x^4+106x^3+115x^2+169x+105$
• $y^2=114x^6+29x^5+86x^4+52x^3+134x^2+89x+176$
• $y^2=71x^6+148x^5+21x^4+86x^3+175x^2+176x+122$
• $y^2=73x^6+25x^5+188x^4+63x^3+35x^2+177x+44$
• $y^2=82x^6+8x^5+136x^4+132x^3+102x^2+100x+148$
• $y^2=9x^6+158x^5+55x^4+9x^3+139x^2+149x+34$
• $y^2=90x^6+131x^5+36x^4+101x^3+121x^2+141x+77$
• $y^2=129x^6+108x^5+104x^4+82x^3+15x^2+107x+160$
• $y^2=114x^6+60x^5+46x^4+108x^3+180x^2+102x+94$
• $y^2=188x^6+147x^5+57x^4+183x^3+183x^2+120x+114$
• $y^2=10x^6+170x^5+181x^4+150x^3+38x^2+10x+9$
• $y^2=75x^6+180x^5+45x^4+102x^3+67x^2+34x+60$
• $y^2=81x^6+123x^5+83x^4+154x^3+140x^2+88x+46$
• $y^2=146x^6+172x^5+162x^4+83x^3+120x^2+108x+99$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28223 1316744065 48549232145648 1771284149156601625 64615450811499098454983 2357222793997147662403068160 85993802976510131366451921168503 3137139829116933059149590566099291625 114445997946589613050534505805565532049008 4175104451009245959774143842147430281923816625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36092 6967584 1330928628 254196485904 48551251429982 9273284518649904 1771197288144967588 338298681564432991584 64615048177564116016652

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.az $\times$ 1.191.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_ahl $2$ (not in LMFDB) 2.191.c_ahl $2$ (not in LMFDB) 2.191.bw_bkv $2$ (not in LMFDB)