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

• Label: 2.191.abv_bjm
• 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:	$( 1 - 27 x + 191 x^{2} )( 1 - 20 x + 191 x^{2} )$
	$1 - 47 x + 922 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0686610702072$, $\pm0.242497774430$
Angle rank:	$2$ (numerical)
Jacobians:	$56$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28380$	$1317626640$	$48545985795120$	$1771230810646440000$	$64615128331508560294500$

Point counts of the curve

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

Jacobians and polarizations

This isogeny class contains the Jacobians of 56 curves (of which all are hyperelliptic), 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

• $y^2=180x^6+129x^5+111x^4+66x^3+17x^2+108x+35$
• $y^2=29x^6+156x^5+104x^4+102x^3+13x^2+155x+153$
• $y^2=42x^6+177x^5+176x^4+164x^3+148x^2+187x+178$
• $y^2=142x^6+103x^5+90x^4+126x^3+105x^2+53x+127$
• $y^2=154x^6+76x^5+185x^4+18x^3+57x^2+136x+129$
• $y^2=x^6+2x^5+127x^4+58x^3+176x^2+89x+165$
• $y^2=137x^6+39x^5+163x^4+146x^3+26x^2+119x+84$
• $y^2=149x^6+42x^5+24x^4+15x^3+42x^2+94x+80$
• $y^2=171x^6+167x^5+159x^4+61x^3+108x^2+159x+173$
• $y^2=19x^6+127x^5+88x^4+156x^3+12x^2+137x+119$
• $y^2=141x^6+24x^5+75x^4+40x^3+146x^2+89x+187$
• $y^2=96x^6+100x^5+30x^4+127x^3+7x^2+82x+57$
• $y^2=70x^6+81x^5+63x^4+47x^3+28x^2+90x+76$
• $y^2=5x^6+164x^5+86x^4+172x^3+182x^2+179x+155$
• $y^2=77x^6+95x^5+75x^4+19x^3+146x^2+96x+17$
• $y^2=43x^6+54x^5+57x^4+152x^3+21x^2+125x+143$
• $y^2=169x^6+33x^5+182x^4+179x^3+160x^2+159x+144$
• $y^2=189x^6+173x^5+63x^4+24x^3+155x^2+145x+89$
• $y^2=93x^6+87x^5+57x^4+18x^3+155x^2+24x+132$
• $y^2=62x^6+74x^5+159x^4+160x^3+83x^2+27x+188$
• $y^2=167x^6+132x^5+76x^4+182x^3+163x^2+82x+117$
• $y^2=129x^6+70x^5+93x^4+91x^3+45x^2+49x+81$
• $y^2=85x^6+82x^5+43x^4+88x^3+105x^2+86x+7$
• $y^2=104x^6+29x^5+130x^4+80x^3+14x^2+145x+142$
• $y^2=107x^6+64x^5+152x^4+12x^3+138x^2+85x+181$
• $y^2=18x^6+143x^5+92x^4+x^3+60x^2+172x+83$
• $y^2=121x^6+130x^5+126x^4+167x^3+67x^2+108x+61$
• $y^2=15x^6+152x^5+26x^4+151x^3+130x^2+114x+150$
• $y^2=155x^6+29x^5+151x^4+5x^3+66x^2+161x+28$
• $y^2=157x^6+18x^5+9x^4+111x^3+57x^2+162x+147$
• $y^2=109x^6+169x^5+90x^4+107x^3+81x^2+100x+6$
• $y^2=133x^6+76x^5+57x^4+10x^3+150x^2+138x+55$
• $y^2=56x^6+146x^5+149x^4+29x^3+66x^2+74x+126$
• $y^2=159x^6+36x^5+15x^4+51x^3+20x^2+52x+184$
• $y^2=188x^6+104x^5+33x^4+110x^3+106x^2+20x+5$
• $y^2=152x^6+171x^5+133x^4+16x^3+145x^2+135x+92$

Decomposition and endomorphism algebra

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

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:

• 1.191.abb : \(\Q(\sqrt{-35}) \).
• 1.191.au : \(\Q(\sqrt{-91}) \).

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)