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

• Label: 2.191.aby_bmq
• 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:	$1 - 50 x + 1004 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.0818372106519$, $\pm0.181493323579$
Angle rank:	$2$ (numerical)
Number field:	4.0.1583424.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27886$	$1313040196$	$48529985415334$	$1771210451423302864$	$64615221602584588672726$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$142$	$35990$	$6964822$	$1330873254$	$254195584202$	$48551239274726$	$9273284388935282$	$1771197287295783934$	$338298681569488144462$	$64615048177881495172550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=75x^6+128x^5+165x^4+111x^3+35x^2+150x+115$
• $y^2=143x^6+98x^5+11x^4+36x^3+109x^2+162x+127$
• $y^2=82x^6+30x^5+2x^4+18x^3+124x^2+33x+71$
• $y^2=5x^6+132x^5+145x^4+134x^3+160x^2+182x+157$
• $y^2=158x^6+97x^5+45x^4+151x^2+119x+27$
• $y^2=142x^6+131x^5+7x^4+167x^3+142x^2+129x+93$
• $y^2=164x^6+4x^5+164x^4+134x^3+26x^2+160x+106$
• $y^2=41x^6+174x^5+54x^4+143x^3+102x^2+20x+122$
• $y^2=81x^6+163x^5+126x^4+133x^3+137x^2+111x+77$
• $y^2=61x^6+93x^5+4x^4+80x^3+152x^2+171x+18$
• $y^2=146x^6+73x^5+90x^4+14x^3+29x^2+166x+86$
• $y^2=93x^6+155x^5+188x^4+190x^3+100x^2+184x+146$
• $y^2=154x^6+163x^5+44x^4+156x^3+137x^2+91x+37$
• $y^2=122x^5+92x^4+104x^3+75x^2+186x+45$

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 4.0.1583424.1.

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.by_bmq	$2$	(not in LMFDB)