Abelian variety isogeny class 2.167.abv_bhz over $\F_{167}$

• Label: 2.167.abv_bhz
• Base field: $\F_{167}$
• 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:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$1 - 47 x + 883 x^{2} - 7849 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0653585255984$, $\pm0.182853389423$
Angle rank:	$2$ (numerical)
Number field:	4.0.925613.1
Galois group:	$D_{4}$
Jacobians:	$9$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20877$	$765538713$	$21678615651267$	$604966396090831389$	$16871969707024828628112$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$27447$	$4654597$	$777795395$	$129892307276$	$21691967385051$	$3622557647310527$	$604967117254049395$	$101029508529127859407$	$16871927924826638687262$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 9 curves (of which all are hyperelliptic):

• $y^2=53 x^6+110 x^5+92 x^4+11 x^3+90 x^2+84 x+139$
• $y^2=35 x^6+166 x^5+69 x^4+31 x^3+117 x^2+157 x+117$
• $y^2=101 x^6+128 x^5+159 x^4+133 x^3+6 x^2+76 x+97$
• $y^2=23 x^6+94 x^5+157 x^4+9 x^3+101 x^2+155 x+149$
• $y^2=10 x^6+120 x^5+160 x^4+77 x^3+123 x^2+64 x+143$
• $y^2=49 x^6+104 x^5+100 x^4+27 x^3+113 x^2+148 x+126$
• $y^2=74 x^6+8 x^5+13 x^4+114 x^3+141 x^2+26 x+161$
• $y^2=140 x^6+37 x^5+18 x^4+165 x^3+34 x^2+22 x+102$
• $y^2=8 x^6+124 x^5+153 x^4+112 x^3+65 x^2+96 x+9$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$

The endomorphism algebra of this simple isogeny class is 4.0.925613.1.

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
2.167.bv_bhz	$2$	(not in LMFDB)