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

• Label: 2.167.abs_bfj
• 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:	$1 - 44 x + 815 x^{2} - 7348 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.129626007809$, $\pm0.213078493916$
Angle rank:	$2$ (numerical)
Number field:	4.0.3881232.1
Galois group:	$D_{4}$
Jacobians:	$10$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$21313$	$769335361$	$21693607639252$	$605008436774593801$	$16872061599337792562833$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$124$	$27584$	$4657816$	$777849444$	$129893014724$	$21691974703574$	$3622557705104588$	$604967117573671108$	$101029508530485421960$	$16871927924846088300704$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=37x^6+46x^5+15x^4+74x^3+85x^2+138x+158$
• $y^2=141x^6+99x^5+123x^4+101x^3+39x^2+30x+154$
• $y^2=83x^6+161x^5+58x^4+130x^3+5x^2+48x+105$
• $y^2=58x^6+12x^5+26x^4+137x^3+86x^2+12x+77$
• $y^2=115x^6+53x^5+25x^4+127x^3+163x^2+101x+108$
• $y^2=32x^6+23x^5+126x^4+123x^3+153x^2+75x+151$
• $y^2=17x^6+135x^5+55x^4+86x^3+9x^2+86x+43$
• $y^2=63x^6+131x^5+9x^4+45x^3+130x^2+137x+60$
• $y^2=33x^6+109x^5+155x^4+96x^3+17x^2+56x+133$
• $y^2=34x^6+116x^5+61x^4+131x^3+28x^2+14x+35$

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 4.0.3881232.1.

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.bs_bfj	$2$	(not in LMFDB)