# Properties

 Label 2.191.abv_bjm 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: $( 1 - 27 x + 191 x^{2} )( 1 - 20 x + 191 x^{2} )$ Frobenius angles: $\pm0.0686610702072$, $\pm0.242497774430$ Angle rank: $2$ (numerical) Jacobians: 56

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 56 curves, and hence is principally polarizable:

• $y^2=82x^6+163x^5+13x^4+68x^3+171x^2+160x+186$
• $y^2=158x^6+65x^5+93x^4+106x^3+97x^2+84x+51$
• $y^2=4x^6+160x^5+126x^4+49x^3+36x^2+138x+22$
• $y^2=164x^6+13x^5+11x^4+126x^3+29x^2+103x+134$
• $y^2=140x^6+115x^5+12x^4+67x^3+133x^2+124x+153$
• $y^2=6x^6+189x^5+135x^4+130x^3+65x^2+125x+23$
• $y^2=169x^6+53x^5+60x^4+124x^3+59x^2+97x+26$
• $y^2=121x^6+62x^5+31x^4+68x^3+111x^2+147x+141$
• $y^2=158x^6+62x^5+177x^4+42x^3+108x^2+68x+145$
• $y^2=43x^6+116x^5+29x^4+117x^3+15x^2+112x+6$
• $y^2=55x^6+13x^5+83x^4+70x^3+130x^2+40x+114$
• $y^2=122x^6+143x^5+35x^4+109x^3+150x^2+181x+21$
• $y^2=91x^6+39x^5+21x^4+16x^3+105x^2+140x+121$
• $y^2=57x^6+117x^5+10x^4+61x^3+24x^2+65x+29$
• $y^2=175x^6+155x^5+79x^4+62x^3+65x^2+46x+6$
• $y^2=60x^6+63x^5+20x^4+110x^3+89x^2+65x+189$
• $y^2=x^6+174x^5+6x^4+63x^3+183x^2+10x+158$
• $y^2=61x^6+55x^5+2x^4+17x^3+36x^2+58x+157$
• $y^2=152x^6+10x^5+124x^4+51x^3+23x^2+107x+147$
• $y^2=110x^6+10x^5+82x^4+95x^3+151x^2+11x+36$
• and 36 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28380 1317626640 48545985795120 1771230810646440000 64615128331508560294500 2357221483191554677050312960 85993799042228598890905835228820 3137139820797983078389802988251040000 114445997938997081888210383357938972354480 4175104451040063199201578635538579059228106000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 145 36117 6967120 1330888553 254195217275 48551224431582 9273284094390125 1771197283448172913 338298681541989714160 64615048178041051967277

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The isogeny class factors as 1.191.abb $\times$ 1.191.au 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.ah_agc $2$ (not in LMFDB) 2.191.h_agc $2$ (not in LMFDB) 2.191.bv_bjm $2$ (not in LMFDB)