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

• Label: 2.191.aca_boq
• 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:	$1 - 52 x + 1056 x^{2} - 9932 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0407629633776$, $\pm0.151065030898$
Angle rank:	$2$ (numerical)
Number field:	4.0.127232.1
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27554$	$1309421188$	$48511750095746$	$1771143887259580688$	$64615026883385448761794$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$140$	$35890$	$6962204$	$1330823238$	$254194818180$	$48551229589618$	$9273284287283156$	$1771197286380083454$	$338298681560338287596$	$64615048177716028815090$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=128x^6+128x^5+69x^4+122x^3+171x^2+68x+151$
• $y^2=63x^6+43x^4+187x^3+26x^2+189x+76$
• $y^2=49x^6+77x^5+142x^4+187x^3+80x^2+60x+190$
• $y^2=21x^6+8x^5+74x^4+104x^3+46x^2+54x+141$

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 4.0.127232.1.

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.ca_boq	$2$	(not in LMFDB)