# Properties

 Label 2.191.aby_bmt 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: $( 1 - 25 x + 191 x^{2} )^{2}$ Frobenius angles: $\pm0.140267993779$, $\pm0.140267993779$ Angle rank: $1$ (numerical) Jacobians: 21

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 21 curves, and hence is principally polarizable:

• $y^2=178x^6+43x^5+121x^4+47x^3+37x^2+71x+93$
• $y^2=96x^6+68x^5+64x^4+163x^3+7x^2+68x+11$
• $y^2=160x^6+59x^5+129x^4+110x^3+135x^2+185x+49$
• $y^2=50x^6+52x^5+25x^4+172x^3+25x^2+52x+50$
• $y^2=58x^6+9x^5+48x^4+78x^3+40x^2+74x+171$
• $y^2=91x^6+176x^5+6x^4+64x^3+6x^2+176x+91$
• $y^2=123x^6+125x^5+63x^4+96x^3+63x^2+125x+123$
• $y^2=169x^6+150x^5+97x^4+67x^3+97x^2+150x+169$
• $y^2=146x^6+151x^5+163x^4+182x^3+26x^2+12x+5$
• $y^2=56x^6+139x^5+144x^4+158x^3+144x^2+139x+56$
• $y^2=155x^6+70x^5+139x^4+164x^3+139x^2+70x+155$
• $y^2=137x^6+128x^5+172x^4+52x^3+172x^2+128x+137$
• $y^2=164x^6+104x^5+49x^4+100x^3+79x+153$
• $y^2=x^6+92x^5+150x^4+77x^3+145x^2+167x+105$
• $y^2=33x^6+123x^5+62x^4+189x^3+62x^2+123x+33$
• $y^2=178x^6+173x^5+87x^4+48x^3+3x^2+38x+112$
• $y^2=170x^6+190x^5+16x^4+71x^3+16x^2+190x+170$
• $y^2=84x^6+22x^5+35x^4+10x^3+35x^2+22x+84$
• $y^2=167x^6+134x^5+18x^4+14x^3+18x^2+134x+167$
• $y^2=127x^6+174x^5+108x^4+139x^3+108x^2+174x+127$
• $y^2=179x^6+4x^5+102x^4+33x^3+47x^2+107x+149$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27889 1313265121 48533125431184 1771234321111425625 64615351242614110697929 2357222761669014187505971456 85993803755390704220551980623449 3137139833444958204159608891993675625 114445997961845435511963596960277825980944 4175104451049335537166318161729395034795513041

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 142 35996 6965272 1330891188 254196094202 48551250764126 9273284602641782 1771197290588526628 338298681609528711112 64615048178184553182956

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-139})$$$)$
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_ajj $2$ (not in LMFDB) 2.191.by_bmt $2$ (not in LMFDB) 2.191.z_qs $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.191.a_ajj $2$ (not in LMFDB) 2.191.by_bmt $2$ (not in LMFDB) 2.191.z_qs $3$ (not in LMFDB) 2.191.a_jj $4$ (not in LMFDB) 2.191.az_qs $6$ (not in LMFDB)