# Properties

 Label 2.191.aby_bms 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: $( 1 - 26 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$ Frobenius angles: $\pm0.110219473395$, $\pm0.165219579186$ Angle rank: $2$ (numerical) Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=37x^6+69x^5+87x^4+4x^3+87x^2+69x+37$
• $y^2=159x^6+82x^5+161x^4+92x^3+37x^2+53x+37$
• $y^2=33x^6+x^5+19x^4+166x^3+19x^2+x+33$
• $y^2=186x^6+148x^5+94x^4+130x^3+94x^2+148x+186$
• $y^2=186x^6+48x^5+188x^4+103x^3+111x^2+8x+190$
• $y^2=159x^6+167x^5+52x^4+39x^3+x^2+152x+190$
• $y^2=146x^6+76x^5+110x^4+164x^3+137x^2+55x+114$
• $y^2=125x^6+36x^5+74x^4+6x^3+74x^2+36x+125$
• $y^2=114x^6+71x^5+117x^4+73x^3+117x^2+71x+114$
• $y^2=151x^6+88x^5+70x^4+84x^3+70x^2+88x+151$
• $y^2=28x^6+115x^5+160x^4+78x^3+160x^2+115x+28$
• $y^2=105x^6+164x^5+110x^4+56x^3+164x^2+188x+110$
• $y^2=45x^6+57x^5+139x^4+166x^3+165x^2+62x+125$
• $y^2=176x^6+42x^5+123x^4+131x^3+123x^2+42x+176$
• $y^2=48x^6+62x^5+74x^4+174x^3+167x^2+88x+59$
• $y^2=83x^6+115x^5+77x^4+53x^3+103x^2+158x+22$
• $y^2=190x^6+57x^5+65x^4+187x^3+65x^2+57x+190$
• $y^2=115x^6+47x^5+134x^4+125x^3+134x^2+47x+115$
• $y^2=69x^6+74x^5+174x^4+25x^3+174x^2+74x+69$
• $y^2=127x^6+8x^5+160x^4+128x^3+59x^2+121x+111$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27888 1313190144 48532078753200 1771226369864146944 64615308156361728468528 2357222577326361061057440000 85993803108915737884757379086448 3137139831598782921868545048276762624 114445997957895256771082915698280749330800 4175104451045616280079780861295669540591638784

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 142 35994 6965122 1330885214 254195924702 48551246967258 9273284532928082 1771197289546194814 338298681597852110062 64615048178126992952154

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.aba $\times$ 1.191.ay 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_aji $2$ (not in LMFDB) 2.191.c_aji $2$ (not in LMFDB) 2.191.by_bms $2$ (not in LMFDB)