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

• Label: 2.191.abz_bnr
• 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:	$1 - 51 x + 1031 x^{2} - 9741 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0868510022643$, $\pm0.156123474003$
Angle rank:	$2$ (numerical)
Number field:	4.0.235125.1
Galois group:	$D_{4}$
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27721$	$1311341905$	$48522457818391$	$1771189516466739405$	$64615193426209723711216$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$141$	$35943$	$6963741$	$1330857523$	$254195473356$	$48551240857443$	$9273284466607071$	$1771197289069510003$	$338298681598843301451$	$64615048178246931323598$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=182x^6+119x^5+45x^4+155x^3+134x^2+175x+107$
• $y^2=175x^6+47x^5+146x^4+159x^3+101x^2+2x+148$
• $y^2=181x^6+126x^5+83x^4+127x^3+95x^2+127x+12$
• $y^2=123x^6+145x^5+171x^4+133x^3+118x^2+109x+86$
• $y^2=12x^6+170x^5+32x^4+36x^3+68x^2+178x+94$
• $y^2=186x^6+92x^5+19x^4+14x^3+84x^2+86x+33$
• $y^2=151x^6+140x^5+118x^4+148x^3+133x^2+100x+126$
• $y^2=74x^6+122x^5+168x^4+25x^3+28x^2+126x+74$

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 4.0.235125.1.

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.bz_bnr	$2$	(not in LMFDB)