# Properties

 Label 2.191.abw_bks 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: $( 1 - 26 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$ Frobenius angles: $\pm0.110219473395$, $\pm0.206981219725$ Angle rank: $2$ (numerical) Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=131x^6+86x^5+87x^4+92x^3+187x^2+177x+176$
• $y^2=38x^6+27x^5+189x^4+55x^3+165x^2+135x+85$
• $y^2=190x^6+41x^5+7x^4+81x^3+113x^2+36x+92$
• $y^2=93x^6+101x^5+36x^4+122x^3+60x^2+157x+140$
• $y^2=35x^6+127x^5+78x^4+113x^3+15x^2+105x+91$
• $y^2=92x^6+66x^5+106x^4+154x^3+106x^2+66x+92$
• $y^2=24x^6+112x^5+187x^4+167x^3+21x^2+6x+170$
• $y^2=176x^6+151x^5+164x^4+79x^3+164x^2+151x+176$
• $y^2=124x^6+45x^5+48x^4+57x^3+104x^2+48x+50$
• $y^2=116x^6+171x^5+39x^4+40x^3+172x^2+131x+139$
• $y^2=155x^6+124x^5+77x^4+150x^3+136x^2+188x+105$
• $y^2=188x^6+181x^5+178x^4+86x^3+x^2+179x+50$
• $y^2=149x^6+112x^5+190x^4+27x^3+190x^2+112x+149$
• $y^2=4x^6+172x^5+98x^4+83x^3+136x^2+163x+1$
• $y^2=49x^6+132x^5+11x^4+149x^3+14x^2+64x+117$
• $y^2=93x^6+102x^5+59x^4+58x^3+163x^2+185x+36$
• $y^2=162x^6+51x^5+155x^4+17x^3+45x^2+164x+145$
• $y^2=7x^6+116x^5+58x^4+155x^3+142x^2+33x+124$
• $y^2=171x^6+168x^5+86x^4+69x^3+86x^2+168x+171$
• $y^2=45x^6+6x^5+169x^4+54x^3+126x^2+132x+142$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28220 1316519440 48546218097020 1771262611568296960 64615343927199401685500 2357222391444081281408554000 85993801820228015174863848245180 3137139826877520012295100310355722240 114445997946079346068453192529234692526780 4175104451028668523346007002184744155763626000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36086 6967152 1330912446 254196065424 48551243138678 9273284393960304 1771197286880617726 338298681562924658832 64615048177864704875126

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.aba $\times$ 1.191.aw 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.ae_ahi $2$ (not in LMFDB) 2.191.e_ahi $2$ (not in LMFDB) 2.191.bw_bks $2$ (not in LMFDB)