Abelian variety isogeny class 2.43.aw_hx over $\F_{43}$

• Label: 2.43.aw_hx
• Base field: $\F_{43}$
• 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:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$1 - 22 x + 205 x^{2} - 946 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.104517857014$, $\pm0.239096202894$
Angle rank:	$2$ (numerical)
Number field:	4.0.91712.2
Galois group:	$D_{4}$
Jacobians:	$3$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1087$	$3286001$	$6324909508$	$11697509645801$	$21614648909244967$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$22$	$1776$	$79552$	$3421524$	$147029982$	$6321457326$	$271818763546$	$11688199646628$	$502592616166960$	$21611482505586496$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which all are hyperelliptic):

• $y^2=26 x^6+20 x^5+32 x^4+2 x^3+11 x^2+20 x+7$
• $y^2=2 x^6+12 x^5+6 x^4+2 x^3+21 x^2+2 x+15$
• $y^2=11 x^6+15 x^5+23 x^4+33 x^3+31 x^2+31 x+4$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{43}$.

Endomorphism algebra over $\F_{43}$

The endomorphism algebra of this simple isogeny class is 4.0.91712.2.

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
2.43.w_hx	$2$	(not in LMFDB)