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

• Label: 2.167.abx_bjx
• 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:	$1 - 49 x + 933 x^{2} - 8183 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.0422800574123$, $\pm0.140113312054$
Angle rank:	$2$ (numerical)
Number field:	4.0.35525.3
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20591$	$762999505$	$21668468942789$	$604937904758306525$	$16871909365461335615056$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$119$	$27355$	$4652417$	$777758763$	$129891842724$	$21691963258615$	$3622557634764887$	$604967117648915523$	$101029508538854049749$	$16871927924946103461150$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which all are hyperelliptic):

• $y^2=43 x^6+x^5+51 x^4+51 x^3+x^2+112 x+161$
• $y^2=49 x^6+38 x^5+10 x^4+156 x^3+59 x^2+53 x+14$
• $y^2=95 x^6+124 x^5+158 x^4+103 x^3+161 x^2+153 x+141$
• $y^2=95 x^6+65 x^5+50 x^4+100 x^3+90 x^2+29 x+145$

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 4.0.35525.3.

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.bx_bjx	$2$	(not in LMFDB)