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 is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):

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

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)