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

• Label: 2.191.abx_blr
• 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:	$1 - 49 x + 979 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0994375871297$, $\pm0.193329123011$
Angle rank:	$2$ (numerical)
Number field:	4.0.3034733.1
Galois group:	$D_{4}$
Jacobians:	$17$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28053$	$1314816057$	$48538603353267$	$1771240131525873213$	$64615300826758128722448$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$143$	$36039$	$6966059$	$1330895555$	$254195895868$	$48551242650795$	$9273284414994505$	$1771197287394715123$	$338298681569195091425$	$64615048177889547775374$

Jacobians and polarizations

This isogeny class contains the Jacobians of 17 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=79x^6+139x^5+114x^4+67x^3+93x^2+69x+50$
• $y^2=146x^6+79x^5+23x^4+81x^3+64x^2+134x+28$
• $y^2=37x^6+99x^5+187x^4+61x^3+140x^2+187x+11$
• $y^2=141x^6+39x^5+65x^4+68x^3+59x^2+15x+70$
• $y^2=185x^6+36x^5+89x^4+168x^3+98x^2+168x+24$
• $y^2=178x^6+124x^5+148x^4+55x^3+34x^2+10x+140$
• $y^2=186x^6+164x^5+28x^4+78x^3+68x^2+91x+29$
• $y^2=25x^6+51x^5+70x^4+172x^3+127x^2+114x+187$
• $y^2=156x^6+85x^5+143x^4+127x^3+60x^2+77x+111$
• $y^2=64x^6+8x^5+25x^4+160x^3+27x^2+121x+123$
• $y^2=165x^6+144x^5+58x^4+24x^3+137x^2+162x+127$
• $y^2=48x^6+154x^5+159x^4+190x^3+90x^2+60x+11$
• $y^2=52x^6+160x^5+184x^4+115x^3+59x^2+182x+76$
• $y^2=15x^6+91x^5+96x^4+156x^3+16x^2+40x+40$
• $y^2=32x^6+100x^5+33x^4+10x^3+53x^2+60x+78$
• $y^2=173x^6+72x^5+139x^4+165x^3+119x^2+186x+72$
• $y^2=109x^6+46x^5+30x^4+125x^3+110x^2+37x+84$

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 4.0.3034733.1.

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.bx_blr	$2$	(not in LMFDB)