Abelian variety isogeny class 2.191.abw_bkk over $\F_{191}$

• Label: 2.191.abw_bkk
• Base field: $\F_{191}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$1 - 48 x + 946 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0359858559519$, $\pm0.233419945036$
Angle rank:	$2$ (numerical)
Number field:	4.0.7488.1
Galois group:	$D_{4}$
Jacobians:	$62$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28212$	$1315920528$	$48538180885428$	$1771204944078655488$	$64615053534038868452532$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36070$	$6966000$	$1330869118$	$254194923024$	$48551219706598$	$9273284004033648$	$1771197281572939774$	$338298681505284405648$	$64615048177408841404390$

Jacobians and polarizations

This isogeny class contains the Jacobians of 62 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=40x^6+179x^5+140x^4+61x^3+96x^2+10x+22$
• $y^2=153x^6+173x^5+49x^4+161x^3+183x^2+45x+139$
• $y^2=151x^6+104x^5+128x^4+50x^3+172x^2+175x+59$
• $y^2=166x^6+76x^5+84x^4+98x^3+157x^2+150x+104$
• $y^2=101x^6+2x^5+179x^4+81x^3+60x^2+152x+153$
• $y^2=112x^6+125x^5+108x^4+50x^3+57x^2+27x+82$
• $y^2=159x^6+120x^5+106x^4+100x^3+93x^2+175x+143$
• $y^2=107x^6+135x^5+141x^4+40x^3+101x^2+114x+87$
• $y^2=41x^6+106x^5+79x^4+131x^3+102x^2+36x+167$
• $y^2=92x^6+127x^5+161x^4+31x^3+61x^2+147x+166$
• $y^2=85x^6+89x^5+97x^4+103x^3+55x^2+60x+81$
• $y^2=132x^6+121x^5+181x^4+181x^3+5x^2+127x+99$
• $y^2=108x^6+178x^5+188x^4+149x^3+110x^2+96x+90$
• $y^2=130x^6+138x^5+60x^4+45x^3+138x^2+8x+146$
• $y^2=142x^6+20x^5+70x^4+39x^3+49x^2+30x+121$
• $y^2=142x^6+131x^5+27x^4+53x^3+36x^2+63x+157$
• $y^2=12x^6+106x^5+13x^4+44x^3+26x^2+80x+75$
• $y^2=46x^6+182x^5+131x^4+160x^3+151x^2+68x+74$
• $y^2=121x^6+93x^5+114x^4+75x^3+37x^2+45x+3$
• $y^2=83x^6+179x^5+147x^4+150x^3+62x^2+85x+56$
• and

• $y^2=143x^6+57x^5+162x^4+169x^3+39x^2+107x+175$
• $y^2=143x^6+126x^5+62x^4+104x^3+56x^2+187x+38$
• $y^2=80x^6+18x^5+6x^4+55x^3+53x^2+172x+10$
• $y^2=152x^6+85x^5+121x^4+178x^3+133x^2+75x+173$
• $y^2=91x^6+30x^5+13x^4+136x^3+41x^2+154x+190$
• $y^2=152x^6+96x^5+134x^4+111x^3+91x^2+24x+167$
• $y^2=71x^6+7x^5+150x^4+120x^3+175x^2+99x+100$
• $y^2=77x^6+10x^5+111x^4+127x^3+49x^2+30x+135$
• $y^2=83x^6+47x^5+46x^4+32x^3+159x^2+91x+178$
• $y^2=15x^6+130x^5+44x^4+85x^3+3x^2+104x+166$
• $y^2=87x^6+174x^5+126x^4+68x^3+170x^2+35x+164$
• $y^2=129x^6+187x^5+114x^4+21x^3+49x^2+106x+53$
• $y^2=36x^6+67x^5+109x^4+5x^3+124x^2+168x+45$
• $y^2=180x^6+171x^5+65x^4+187x^3+178x^2+115x+66$
• $y^2=49x^6+x^5+128x^4+69x^3+8x^2+29x+117$
• $y^2=106x^6+147x^5+4x^4+123x^3+11x^2+30x+105$
• $y^2=176x^6+40x^5+6x^4+x^3+151x^2+120x+140$
• $y^2=119x^6+182x^5+146x^4+175x^3+36x^2+35x+17$
• $y^2=52x^6+26x^5+187x^4+188x^3+94x^2+45x+142$
• $y^2=24x^6+190x^5+174x^4+4x^3+64x^2+122x+139$
• $y^2=32x^6+45x^5+7x^4+24x^3+13x^2+28x+33$
• $y^2=49x^6+92x^5+34x^4+152x^3+50x^2+8x+152$
• $y^2=124x^6+146x^5+74x^4+160x^3+172x^2+143x+29$
• $y^2=171x^6+37x^5+11x^4+52x^3+72x+38$
• $y^2=105x^6+116x^5+133x^4+8x^3+87x^2+15x+162$
• $y^2=69x^6+182x^5+38x^4+174x^3+2x^2+18x+190$
• $y^2=11x^6+157x^5+36x^4+168x^3+72x^2+23x+24$
• $y^2=14x^6+178x^5+173x^4+57x^3+121x^2+155x+183$
• $y^2=82x^6+188x^5+12x^4+118x^3+x^2+185x+68$
• $y^2=164x^6+54x^5+27x^4+121x^3+150x^2+104x+82$
• $y^2=14x^6+92x^5+51x^4+38x^3+21x^2+65x+34$
• $y^2=83x^6+66x^5+174x^4+52x^3+135x^2+153x+172$
• $y^2=46x^6+65x^5+11x^4+61x^3+136x^2+41x+119$
• $y^2=40x^6+60x^5+154x^4+46x^3+52x^2+148x+114$
• $y^2=164x^6+122x^5+119x^4+4x^3+88x^2+168x+35$
• $y^2=28x^6+146x^5+47x^4+9x^3+78x^2+42x+114$
• $y^2=153x^6+178x^5+23x^4+92x^3+62x^2+60x+80$
• $y^2=140x^6+122x^5+54x^4+129x^3+127x^2+44x+101$
• $y^2=88x^6+150x^5+87x^4+81x^3+8x^2+94x+106$
• $y^2=172x^6+156x^5+20x^4+152x^3+4x^2+165x+120$
• $y^2=41x^6+171x^5+38x^4+157x^3+120x^2+127x+176$
• $y^2=171x^6+151x^5+104x^4+124x^3+22x^2+96x+62$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{191}$.

Endomorphism algebra over $\F_{191}$

The endomorphism algebra of this simple isogeny class is 4.0.7488.1.

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_bkk	$2$	(not in LMFDB)