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

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

Invariants

Base field:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 191 x^{2} )^{2}$
	$1 - 48 x + 958 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.165219579186$, $\pm0.165219579186$
Angle rank:	$1$ (numerical)
Jacobians:	$105$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28224$	$1316818944$	$48550236840000$	$1771291317720121344$	$64615486195582895006784$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$144$	$36094$	$6967728$	$1330934014$	$254196625104$	$48551254133758$	$9273284557619184$	$1771197288479817214$	$338298681562582691088$	$64615048177410656806654$

Jacobians and polarizations

This isogeny class contains the Jacobians of 105 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=57x^6+158x^5+177x^4+87x^3+72x^2+51x+76$
• $y^2=28x^6+47x^5+8x^4+106x^3+8x^2+47x+28$
• $y^2=24x^6+183x^5+179x^4+149x^3+173x^2+173x+81$
• $y^2=186x^6+180x^5+173x^4+28x^3+38x^2+17x+57$
• $y^2=61x^6+38x^4+38x^2+61$
• $y^2=55x^6+31x^5+132x^4+107x^3+162x^2+168$
• $y^2=41x^6+164x^5+35x^4+8x^3+38x^2+123x+178$
• $y^2=14x^6+87x^5+70x^4+109x^3+70x^2+87x+14$
• $y^2=189x^6+61x^5+113x^4+108x^3+71x^2+89x+88$
• $y^2=24x^6+39x^5+113x^4+47x^3+94x^2+135x+144$
• $y^2=26x^6+64x^5+180x^4+179x^3+177x^2+50x+15$
• $y^2=150x^6+94x^5+26x^4+180x^3+26x^2+94x+150$
• $y^2=114x^6+110x^5+3x^4+144x^3+3x^2+110x+114$
• $y^2=7x^6+68x^5+49x^4+165x^3+49x^2+68x+7$
• $y^2=111x^6+77x^5+65x^4+180x^3+65x^2+77x+111$
• $y^2=132x^6+43x^5+17x^4+68x^3+149x^2+10x+152$
• $y^2=190x^6+93x^5+186x^4+33x^3+73x^2+21x+76$
• $y^2=94x^6+80x^5+130x^4+36x^3+169x^2+131x+67$
• $y^2=125x^6+146x^5+87x^4+25x^3+87x^2+146x+125$
• $y^2=163x^6+148x^4+148x^2+163$
• and

• $y^2=161x^6+24x^5+84x^4+16x^3+84x^2+24x+161$
• $y^2=132x^6+31x^5+122x^4+105x^3+57x^2+132x+31$
• $y^2=60x^6+59x^5+37x^4+155x^3+73x^2+150x+102$
• $y^2=175x^6+182x^5+126x^4+105x^3+101x^2+11x+174$
• $y^2=59x^6+180x^5+167x^4+177x^3+189x^2+49x+49$
• $y^2=79x^6+140x^5+48x^4+143x^3+48x^2+140x+79$
• $y^2=66x^6+13x^4+13x^2+66$
• $y^2=147x^6+46x^5+120x^4+103x^3+177x^2+54x+109$
• $y^2=152x^6+157x^5+104x^4+163x^3+104x^2+157x+152$
• $y^2=157x^6+24x^5+166x^4+60x^3+166x^2+24x+157$
• $y^2=99x^6+129x^5+108x^4+117x^3+13x^2+149x+139$
• $y^2=81x^6+176x^4+176x^2+81$
• $y^2=167x^6+x^5+76x^4+124x^3+66x^2+103x+95$
• $y^2=17x^6+55x^5+38x^4+77x^3+91x^2+101x+86$
• $y^2=105x^6+22x^5+93x^4+42x^3+93x^2+22x+105$
• $y^2=133x^6+9x^5+175x^4+3x^3+152x^2+96x+20$
• $y^2=150x^6+166x^4+166x^2+150$
• $y^2=47x^6+108x^4+108x^2+47$
• $y^2=69x^6+45x^4+45x^2+69$
• $y^2=14x^6+37x^5+65x^4+91x^3+149x^2+89x+142$
• $y^2=116x^6+118x^5+166x^4+101x^3+166x^2+118x+116$
• $y^2=170x^6+75x^5+8x^4+24x^3+138x^2+6x+120$
• $y^2=38x^6+19x^5+50x^4+177x^3+50x^2+19x+38$
• $y^2=122x^6+124x^5+44x^4+98x^3+44x^2+124x+122$
• $y^2=61x^6+145x^5+130x^4+39x^3+98x^2+164x+175$
• $y^2=109x^6+162x^5+97x^4+154x^3+97x^2+162x+109$
• $y^2=89x^6+98x^5+46x^4+32x^3+48x^2+2x+159$
• $y^2=137x^6+87x^4+87x^2+137$
• $y^2=6x^6+179x^5+132x^4+102x^3+132x^2+179x+6$
• $y^2=53x^6+127x^5+179x^4+108x^3+179x^2+127x+53$
• $y^2=69x^6+124x^5+146x^4+100x^3+161x^2+140x+169$
• $y^2=159x^6+16x^5+172x^4+60x^3+71x^2+190x+148$
• $y^2=135x^6+111x^5+173x^4+44x^3+173x^2+111x+135$
• $y^2=9x^6+88x^5+95x^4+30x^3+116x^2+94x+79$
• $y^2=113x^6+157x^5+189x^4+41x^3+189x^2+157x+113$
• $y^2=13x^6+83x^5+132x^4+61x^3+132x^2+83x+13$
• $y^2=17x^6+79x^5+185x^4+70x^3+185x^2+79x+17$
• $y^2=145x^6+107x^5+93x^4+101x^3+93x^2+107x+145$
• $y^2=103x^6+x^5+51x^4+7x^3+51x^2+x+103$
• $y^2=151x^6+170x^5+127x^4+127x^2+170x+151$
• $y^2=110x^6+137x^5+127x^4+20x^3+74x^2+58x+168$
• $y^2=186x^6+177x^4+177x^2+186$
• $y^2=187x^6+190x^5+174x^4+56x^3+174x^2+190x+187$
• $y^2=69x^6+22x^5+137x^4+78x^3+122x^2+182x+106$
• $y^2=44x^6+127x^5+174x^4+187x^3+76x^2+83x+95$
• $y^2=44x^6+32x^5+51x^4+127x^3+43x^2+100x+159$
• $y^2=127x^6+98x^5+186x^4+82x^3+127x^2+104x+95$
• $y^2=55x^6+50x^5+188x^4+119x^3+139x^2+103x+143$
• $y^2=141x^6+76x^5+23x^4+90x^3+6x^2+42x+99$
• $y^2=76x^6+140x^5+75x^4+108x^3+75x^2+140x+76$
• $y^2=145x^6+180x^5+117x^4+12x^3+43x^2+147x+14$
• $y^2=132x^6+130x^5+5x^4+138x^3+163x^2+104x+165$
• $y^2=189x^6+51x^5+188x^4+5x^3+188x^2+51x+189$
• $y^2=164x^6+185x^5+123x^4+120x^3+132x^2+175x+151$
• $y^2=37x^6+159x^5+61x^4+160x^3+61x^2+159x+37$
• $y^2=112x^6+179x^5+42x^4+147x^3+146x^2+33x+139$
• $y^2=189x^6+71x^5+68x^4+121x^3+27x^2+105x+66$
• $y^2=55x^6+14x^5+42x^4+188x^3+42x^2+14x+55$
• $y^2=180x^6+133x^5+142x^4+83x^3+174x^2+10x+143$
• $y^2=153x^6+84x^5+127x^4+177x^3+127x^2+84x+153$
• $y^2=118x^6+44x^5+85x^4+129x^3+6x^2+143x+81$
• $y^2=3x^6+24x^5+62x^4+122x^3+62x^2+24x+3$
• $y^2=16x^6+144x^5+185x^4+45x^3+7x^2+5x+109$
• $y^2=6x^6+40x^5+167x^4+2x^3+167x^2+40x+6$
• $y^2=58x^6+29x^5+25x^4+134x^3+179x^2+45x+6$
• $y^2=125x^6+112x^5+91x^4+57x^3+174x^2+94x+150$
• $y^2=41x^6+25x^5+61x^4+34x^3+82x^2+158x+119$
• $y^2=44x^6+156x^5+21x^4+31x^3+21x^2+156x+44$
• $y^2=102x^6+115x^5+149x^4+87x^3+54x^2+3x+26$
• $y^2=73x^6+78x^5+2x^4+36x^3+94x^2+146x+181$
• $y^2=116x^6+113x^5+163x^4+146x^3+107x^2+186x+32$
• $y^2=174x^6+27x^5+65x^4+127x^3+65x^2+27x+174$
• $y^2=107x^5+95x^4+154x^3+141x^2+18x$
• $y^2=44x^6+150x^5+82x^4+33x^3+82x^2+150x+44$
• $y^2=17x^6+154x^5+88x^4+96x^3+177x^2+61x+29$
• $y^2=4x^6+163x^5+105x^4+10x^3+116x^2+13x+52$
• $y^2=95x^6+59x^4+59x^2+95$
• $y^2=154x^6+172x^5+113x^4+138x^3+113x^2+172x+154$
• $y^2=53x^6+177x^5+50x^4+121x^3+50x^2+177x+53$
• $y^2=115x^6+34x^5+29x^4+33x^3+119x^2+124x+174$
• $y^2=126x^6+55x^5+121x^4+123x^3+121x^2+55x+126$
• $y^2=129x^6+3x^5+164x^4+43x^3+143x^2+59x+96$
• $y^2=132x^6+87x^5+26x^4+104x^3+4x^2+71x+11$
• $y^2=81x^6+119x^5+9x^4+69x^3+9x^2+119x+81$
• $y^2=180x^6+98x^5+22x^4+144x^3+123x^2+177x+77$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.ay^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-47}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.191.a_ahm	$2$	(not in LMFDB)
2.191.bw_bkw	$2$	(not in LMFDB)
2.191.y_ov	$3$	(not in LMFDB)