# Properties

 Label 2.191.aby_bmo 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: $1 - 50 x + 1002 x^{2} - 9550 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.0545220769588$, $\pm0.191978923746$ Angle rank: $2$ (numerical) Number field: 4.0.136400.1 Galois group: $D_{4}$ Jacobians: 24

This isogeny class is simple and geometrically 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:

• $y^2=76x^6+178x^5+65x^4+98x^3+102x^2+66x+159$
• $y^2=165x^6+91x^5+25x^4+42x^3+3x^2+97x+84$
• $y^2=47x^6+29x^5+153x^4+156x^3+100x^2+187x+186$
• $y^2=134x^6+132x^5+168x^4+120x^3+187x^2+22x+117$
• $y^2=45x^6+133x^5+9x^4+82x^3+190x^2+122x+33$
• $y^2=102x^6+x^5+132x^4+50x^3+114x^2+23x+7$
• $y^2=178x^6+125x^5+97x^4+150x^3+17x^2+24x+126$
• $y^2=112x^6+165x^5+151x^4+7x^3+144x^2+143x+79$
• $y^2=186x^6+54x^5+116x^4+26x^3+83x^2+115x+73$
• $y^2=31x^6+141x^5+145x^4+101x^3+153x^2+62x+98$
• $y^2=83x^6+138x^5+25x^4+161x^3+24x^2+182x+92$
• $y^2=168x^6+14x^5+124x^4+56x^3+68x^2+71x+83$
• $y^2=175x^6+64x^5+137x^4+51x^3+71x^2+20x+50$
• $y^2=8x^6+164x^5+37x^4+93x^3+146x^2+181x+132$
• $y^2=119x^6+160x^5+149x^4+17x^3+147x^2+93x+73$
• $y^2=151x^6+127x^5+117x^4+87x^3+116x^2+185x+47$
• $y^2=87x^6+4x^5+120x^4+131x^3+107x^2+150x+148$
• $y^2=142x^6+149x^5+134x^4+138x^3+89x^2+162x+60$
• $y^2=64x^6+171x^5+170x^4+57x^3+188x^2+180x+22$
• $y^2=29x^6+115x^5+18x^4+65x^3+87x^2+56x+119$
• $y^2=17x^6+64x^5+56x^4+25x^3+73x^2+184x+73$
• $y^2=137x^6+177x^5+129x^4+138x^3+36x^2+161x+113$
• $y^2=83x^6+76x^5+133x^4+145x^3+58x^2+165x+53$
• $y^2=65x^6+44x^5+53x^4+58x^3+156x^2+116x+41$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 27884 1312890256 48527892101564 1771194511720582400 64615134540443980747804 2357221823963014166468359696 85993800381765225721498380209804 3137139823233247083236094816925798400 114445997936416658187735806752023229535564 4175104451002399053723510769475922175590086416

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 142 35986 6964522 1330861278 254195241702 48551231450386 9273284238841282 1771197284823098238 338298681534362064862 64615048177458151442706

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.136400.1.
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.by_bmo $2$ (not in LMFDB)