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

• Label: 2.43.ag_ad
• 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:	$1 - 6 x - 3 x^{2} - 258 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0577675548247$, $\pm0.676339342821$
Angle rank:	$2$ (numerical)
Number field:	4.0.44608.1
Galois group:	$D_{4}$
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1583$	$3341713$	$6238786628$	$11686347974569$	$21610581902070263$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$38$	$1808$	$78464$	$3418260$	$147002318$	$6321132974$	$271819002794$	$11688201359140$	$502592571568496$	$21611482600784288$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

• $y^2=20 x^6+33 x^5+12 x^4+25 x^3+19 x^2+2 x+6$
• $y^2=25 x^6+39 x^5+20 x^4+19 x^3+15 x^2+19 x+11$
• $y^2=37 x^6+35 x^5+23 x^4+4 x^3+17 x^2+5 x+6$
• $y^2=37 x^6+2 x^5+39 x^4+4 x^3+34 x^2+29 x+20$
• $y^2=4 x^6+35 x^5+10 x^4+7 x^3+12 x^2+40 x+5$
• $y^2=10 x^6+33 x^5+28 x^4+22 x^3+17 x^2+29 x+37$
• $y^2=34 x^6+x^5+41 x^4+2 x^3+12 x^2+39 x+42$
• $y^2=8 x^6+31 x^5+42 x^4+14 x^3+42 x^2+25 x+15$
• $y^2=25 x^6+10 x^5+31 x^4+40 x^3+28 x^2+31 x+4$
• $y^2=21 x^6+9 x^5+7 x^4+19 x^3+14 x^2+4 x+14$
• $y^2=7 x^6+11 x^5+13 x^4+13 x^3+25 x^2+31 x+38$
• $y^2=20 x^6+27 x^5+39 x^4+10 x^3+12 x^2+42 x+19$
• $y^2=32 x^6+30 x^5+x^4+9 x^3+4 x^2+23 x+3$
• $y^2=35 x^6+3 x^5+24 x^4+26 x^3+22 x^2+19 x+22$
• $y^2=28 x^6+27 x^5+36 x^4+33 x^3+28 x^2+11 x+11$
• $y^2=19 x^6+3 x^5+27 x^4+36 x^3+27 x^2+3 x+30$
• $y^2=13 x^6+42 x^5+30 x^4+28 x^3+4 x^2+34 x+40$
• $y^2=19 x^6+16 x^4+30 x^3+23 x^2+4 x+42$

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 4.0.44608.1.

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.g_ad	$2$	(not in LMFDB)