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

• Label: 2.167.abw_biy
• 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:	$1 - 48 x + 908 x^{2} - 8016 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0582449944782$, $\pm0.161602454123$
Angle rank:	$2$ (numerical)
Number field:	4.0.223488.6
Galois group:	$D_{4}$
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20734$	$764296708$	$21673863449518$	$604954103401290384$	$16871947932450251046574$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$120$	$27402$	$4653576$	$777779590$	$129892139640$	$21691966626186$	$3622557662472456$	$604967117737605310$	$101029508536905351864$	$16871927924903026734762$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):

• $y^2=38 x^6+25 x^5+95 x^4+19 x^3+91 x^2+97 x+56$
• $y^2=120 x^6+3 x^5+28 x^4+33 x^3+77 x^2+139 x+163$
• $y^2=143 x^6+94 x^5+103 x^4+153 x^3+26 x^2+108 x+81$
• $y^2=129 x^6+23 x^5+70 x^4+165 x^3+98 x^2+151 x+4$
• $y^2=14 x^6+17 x^5+30 x^4+31 x^3+21 x^2+128 x+60$
• $y^2=19 x^6+68 x^5+134 x^4+130 x^3+39 x^2+9 x+41$
• $y^2=75 x^6+155 x^5+96 x^4+96 x^3+63 x^2+51 x+55$
• $y^2=106 x^6+106 x^5+19 x^4+5 x^3+40 x^2+66 x+77$

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 4.0.223488.6.

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.bw_biy	$2$	(not in LMFDB)