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

• Label: 2.191.abv_bjl
• 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:	$1 - 47 x + 921 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0606665304000$, $\pm0.244825545542$
Angle rank:	$2$ (numerical)
Number field:	4.0.28463597.1
Galois group:	$D_{4}$
Jacobians:	$21$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28379$	$1317551833$	$48545002152881$	$1771223956304745293$	$64615095058595342610544$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36115$	$6966979$	$1330883403$	$254195086380$	$48551221855063$	$9273284053075621$	$1771197282890356899$	$338298681535345104811$	$64615048177963413520590$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=53x^6+104x^5+62x^4+181x^3+164x^2+8x+92$
• $y^2=137x^6+105x^5+134x^4+180x^3+100x^2+143x+138$
• $y^2=90x^6+175x^5+33x^4+50x^3+59x^2+51x+182$
• $y^2=17x^6+111x^5+8x^4+107x^3+168x^2+42x+61$
• $y^2=180x^6+79x^5+141x^4+95x^3+37x^2+184x+168$
• $y^2=173x^6+180x^5+16x^4+126x^3+43x^2+133x+132$
• $y^2=30x^6+140x^5+154x^4+100x^3+75x^2+187x+151$
• $y^2=159x^6+144x^5+77x^4+33x^3+102x^2+20x+41$
• $y^2=138x^6+125x^5+49x^4+115x^3+188x^2+49x+127$
• $y^2=65x^6+118x^5+23x^4+29x^3+173x^2+121x+109$
• $y^2=110x^6+50x^5+33x^4+145x^3+75x^2+182x+21$
• $y^2=57x^6+171x^5+174x^4+31x^3+122x^2+57x+136$
• $y^2=132x^6+163x^5+78x^4+5x^3+84x^2+22x+152$
• $y^2=160x^6+173x^5+170x^4+90x^3+180x^2+81x+52$
• $y^2=14x^6+162x^5+81x^4+59x^3+60x^2+133x+40$
• $y^2=137x^6+25x^5+150x^4+81x^3+171x^2+113x+15$
• $y^2=164x^6+57x^5+32x^4+185x^3+151x^2+164x+19$
• $y^2=130x^6+114x^5+72x^4+176x^3+130x^2+64x+14$
• $y^2=181x^6+143x^5+115x^4+21x^3+173x^2+109x+144$
• $y^2=45x^6+62x^5+171x^4+187x^3+154x^2+130x+154$
• $y^2=10x^6+16x^5+118x^4+83x^3+60x^2+147x+127$

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 4.0.28463597.1.

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.bv_bjl	$2$	(not in LMFDB)