Properties

 Label 2.191.abw_bkr 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: $1 - 48 x + 953 x^{2} - 9168 x^{3} + 36481 x^{4}$ Frobenius angles: $\pm0.101907512735$, $\pm0.211431110568$ Angle rank: $2$ (numerical) Number field: 4.0.549225.1 Galois group: $D_{4}$ Jacobians: 28

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 28 curves, and hence is principally polarizable:

• $y^2=33x^6+42x^5+74x^4+89x^3+15x^2+11x+100$
• $y^2=91x^6+116x^5+118x^4+82x^3+148x^2+121x+45$
• $y^2=160x^6+89x^5+26x^4+13x^3+5x^2+146x+114$
• $y^2=99x^6+87x^5+136x^4+113x^3+153x^2+43x+174$
• $y^2=82x^6+5x^5+64x^4+138x^3+147x^2+122x+174$
• $y^2=112x^6+162x^5+173x^4+138x^3+82x^2+173x+107$
• $y^2=65x^6+149x^5+129x^4+45x^3+39x^2+19x+134$
• $y^2=21x^6+81x^5+75x^4+58x^3+149x^2+121x+73$
• $y^2=187x^6+141x^5+175x^4+59x^3+113x^2+24x+95$
• $y^2=111x^6+86x^5+89x^4+77x^3+188x^2+189x+114$
• $y^2=66x^6+95x^5+31x^4+83x^3+75x^2+107x+157$
• $y^2=135x^6+63x^5+65x^4+31x^3+24x^2+47x+159$
• $y^2=53x^6+157x^5+131x^4+129x^3+126x^2+180x+168$
• $y^2=58x^6+151x^5+96x^4+156x^3+17x^2+109x+137$
• $y^2=77x^6+55x^5+67x^4+153x^3+141x^2+168x+172$
• $y^2=64x^6+13x^5+6x^4+169x^3+37x^2+119x+62$
• $y^2=117x^6+137x^5+137x^4+75x^3+43x^2+9x+182$
• $y^2=165x^6+75x^5+68x^4+123x^3+181x^2+22x+168$
• $y^2=178x^6+111x^5+167x^4+65x^3+115x^2+50x+24$
• $y^2=180x^6+105x^5+160x^4+146x^3+161x^2+22x+137$
• $y^2=23x^6+115x^5+183x^4+81x^3+76x^2+38x+47$
• $y^2=119x^6+174x^5+135x^4+122x^3+70x^2+95x+117$
• $y^2=152x^6+55x^5+126x^4+168x^3+13x^2+158x+118$
• $y^2=123x^6+92x^5+26x^4+43x^3+157x^2+63x+20$
• $y^2=58x^6+93x^5+80x^4+151x^3+119x^2+133x+136$
• $y^2=137x^6+90x^5+16x^4+177x^3+27x^2+103x+123$
• $y^2=132x^6+186x^5+96x^4+151x^3+99x^2+18x+181$
• $y^2=43x^6+124x^5+38x^4+145x^3+115x^2+70x+154$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28219 1316444569 48545213425600 1771255421739537129 64615308055083265449259 2357222254345104476029849600 85993801410684171669669158195659 3137139825976627643900308084164394569 114445997945101379038014880917267363505600 4175104451031596744408389159085757771428945209

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 144 36084 6967008 1330907044 254195924304 48551240314878 9273284349796464 1771197286371983044 338298681560033819808 64615048177910022818004

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
 The endomorphism algebra of this simple isogeny class is 4.0.549225.1.
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.bw_bkr $2$ (not in LMFDB)