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

• Label: 2.43.as_fw
• 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:	$1 - 18 x + 152 x^{2} - 774 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0612301159281$, $\pm0.372152980887$
Angle rank:	$2$ (numerical)
Number field:	4.0.3297600.1
Galois group:	$D_{4}$
Jacobians:	$16$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1210$	$3380740$	$6325566610$	$11679577707600$	$21606214423395250$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$26$	$1830$	$79562$	$3416278$	$146972606$	$6321180390$	$271818717182$	$11688206879518$	$502592639533706$	$21611482226376150$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=40 x^6+23 x^5+13 x^4+23 x^3+36 x^2+30 x+6$
• $y^2=37 x^6+30 x^5+21 x^4+16 x^3+29 x^2+39 x+12$
• $y^2=13 x^6+4 x^5+21 x^3+18 x^2+27 x+12$
• $y^2=22 x^6+2 x^5+39 x^4+19 x^3+16 x^2+12 x+5$
• $y^2=25 x^6+x^5+19 x^4+18 x^3+23 x^2+12 x+27$
• $y^2=22 x^6+41 x^5+28 x^4+21 x^3+25 x^2+40 x+30$
• $y^2=26 x^6+21 x^5+19 x^4+14 x^3+6 x^2+2 x+27$
• $y^2=15 x^6+x^5+39 x^4+27 x^3+14 x^2+38 x+32$
• $y^2=40 x^6+10 x^5+42 x^4+x^3+2 x^2+27 x+19$
• $y^2=27 x^6+31 x^5+21 x^4+16 x^3+20 x^2+11 x+42$
• $y^2=32 x^6+30 x^5+11 x^4+38 x^3+29 x^2+25 x+26$
• $y^2=28 x^6+3 x^5+4 x^4+7 x^3+40 x^2+30 x+5$
• $y^2=38 x^6+25 x^5+30 x^4+33 x^3+39 x^2+17 x+8$
• $y^2=5 x^6+7 x^5+26 x^4+35 x^3+36 x^2+39 x+32$
• $y^2=10 x^5+20 x^4+6 x^3+12 x^2+34$
• $y^2=22 x^6+13 x^5+15 x^4+23 x^3+13 x^2+5 x+3$

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 4.0.3297600.1.

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
2.43.s_fw	$2$	(not in LMFDB)