# Properties

 Label 2.191.aby_bmp 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: $( 1 - 27 x + 191 x^{2} )( 1 - 23 x + 191 x^{2} )$ Frobenius angles: $\pm0.0686610702072$, $\pm0.187132320568$ Angle rank: $2$ (numerical) Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=183x^6+157x^5+48x^4+111x^3+38x^2+157x+145$
• $y^2=188x^6+144x^5+161x^4+133x^3+35x^2+23x+4$
• $y^2=44x^6+82x^5+162x^4+68x^3+162x^2+82x+44$
• $y^2=172x^6+160x^5+83x^4+52x^3+158x^2+94x+103$
• $y^2=139x^6+62x^5+110x^4+171x^3+110x^2+62x+139$
• $y^2=107x^6+111x^5+186x^4+114x^3+73x^2+32x+148$
• $y^2=132x^6+64x^5+86x^4+143x^3+107x^2+37x+98$
• $y^2=105x^6+117x^5+161x^4+137x^3+51x^2+54x+19$
• $y^2=22x^6+25x^5+66x^4+170x^3+66x^2+25x+22$
• $y^2=42x^6+32x^5+112x^4+141x^3+112x^2+32x+42$
• $y^2=65x^6+23x^5+39x^4+83x^3+173x^2+136x+4$
• $y^2=28x^6+23x^5+66x^4+187x^3+66x^2+23x+28$
• $y^2=148x^6+101x^5+56x^4+141x^3+56x^2+101x+148$
• $y^2=178x^6+103x^5+143x^4+75x^3+143x^2+103x+178$
• $y^2=188x^6+163x^5+20x^4+179x^3+115x^2+26x+186$
• $y^2=160x^6+167x^5+141x^4+145x^3+149x^2+99x+160$
• $y^2=121x^6+25x^5+30x^4+27x^3+30x^2+25x+121$
• $y^2=136x^6+184x^5+95x^4+85x^3+95x^2+184x+136$
• $y^2=60x^6+188x^5+6x^4+150x^3+51x^2+130x+73$
• $y^2=111x^6+112x^5+13x^4+56x^3+36x^2+139x+184$
• $y^2=144x^6+89x^5+128x^4+119x^3+128x^2+89x+144$
• $y^2=163x^6+92x^5+138x^4+135x^3+138x^2+92x+163$
• $y^2=11x^6+110x^5+182x^4+10x^3+3x^2+180x+74$
• $y^2=62x^6+180x^5+43x^4+49x^3+43x^2+180x+62$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27885 1312965225 48528938755440 1771202484229689225 64615178135059740742125 2357222014703926385561145600 85993801084779398672571394192365 3137139825472435623978491604036297225 114445997942646222604358486211305390891760 4175104451017532153406827147668336467369515625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 142 35988 6964672 1330867268 254195413202 48551235379038 9273284314651982 1771197286087321348 338298681552776456512 64615048177692355395348

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.abb $\times$ 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.ae_ajf $2$ (not in LMFDB) 2.191.e_ajf $2$ (not in LMFDB) 2.191.by_bmp $2$ (not in LMFDB)