# Properties

 Label 2.191.aca_bor 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: $( 1 - 27 x + 191 x^{2} )( 1 - 25 x + 191 x^{2} )$ Frobenius angles: $\pm0.0686610702072$, $\pm0.140267993779$ 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:

• $y^2=11x^6+145x^5+9x^4+49x^3+100x^2+84x+73$
• $y^2=120x^6+33x^5+149x^4+66x^3+96x^2+188x+144$
• $y^2=142x^6+71x^5+170x^4+69x^3+177x^2+74x+35$
• $y^2=90x^6+157x^5+153x^4+84x^3+121x^2+137x+80$
• $y^2=78x^6+165x^5+46x^4+69x^3+18x^2+126x+68$
• $y^2=100x^6+149x^5+126x^4+57x^3+112x^2+80x+147$
• $y^2=188x^6+23x^5+88x^4+26x^3+33x^2+48x+89$
• $y^2=23x^6+107x^5+74x^4+180x^3+113x^2+90x+120$
• $y^2=114x^6+106x^5+58x^4+88x^3+145x^2+185x+110$
• $y^2=143x^6+159x^5+8x^4+135x^3+59x^2+74x+174$
• $y^2=162x^6+89x^5+84x^4+82x^3+188x^2+14x+130$
• $y^2=104x^6+76x^5+85x^4+49x^3+5x^2+145x+153$
• $y^2=82x^6+164x^5+177x^4+74x^3+51x^2+165x+61$
• $y^2=101x^6+54x^5+162x^4+110x^3+69x^2+77x+88$
• $y^2=164x^6+47x^5+132x^4+118x^3+124x^2+176x+31$
• $y^2=35x^6+82x^5+28x^4+103x^3+99x^2+55x+37$
• $y^2=182x^6+91x^5+163x^4+82x^3+46x^2+116x+110$
• $y^2=7x^6+36x^5+28x^4+78x^3+47x^2+118x+73$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27555 1309496265 48512838773520 1771152658481831625 64615078566594932503875 2357221982375803598281416960 85993801863659954392502876769795 3137139829800460763960529859056671625 114445997957902045065261917529742477537680 4175104451057621730799081031727027952027871625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 140 35892 6962360 1330829828 254195021500 48551234713182 9273284398643860 1771197288530880388 338298681597872176040 64615048178312792561652

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.abb $\times$ 1.191.az 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_alh $2$ (not in LMFDB) 2.191.c_alh $2$ (not in LMFDB) 2.191.ca_bor $2$ (not in LMFDB)