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

• Label: 2.43.e_dk
• 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:	$1 + 4 x + 88 x^{2} + 172 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.514222296469$, $\pm0.583831798889$
Angle rank:	$2$ (numerical)
Number field:	4.0.1761536.1
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2114$	$3724868$	$6283706450$	$11669519761424$	$21615723044959554$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$48$	$2010$	$79032$	$3413334$	$147037288$	$6321514890$	$271817286096$	$11688197364894$	$502592660739696$	$21611482321541050$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):

• $y^2=23 x^6+30 x^5+31 x^4+14 x^3+31 x^2+39 x+24$
• $y^2=x^6+7 x^5+30 x^4+13 x^3+23 x^2+35 x+7$
• $y^2=36 x^6+20 x^5+17 x^4+24 x^3+17 x^2+21 x+6$
• $y^2=41 x^6+32 x^5+22 x^4+19 x^3+37 x^2+16 x+32$
• $y^2=14 x^6+15 x^5+17 x^4+4 x^3+25 x^2+38 x+22$
• $y^2=6 x^6+31 x^5+19 x^4+15 x^3+21 x^2+9 x+7$
• $y^2=10 x^6+17 x^5+35 x^4+29 x^3+42 x^2+41 x+31$
• $y^2=22 x^6+35 x^5+4 x^4+5 x^3+22 x^2+6 x+25$
• $y^2=26 x^5+40 x^4+9 x^3+36 x^2+11 x+14$
• $y^2=28 x^6+36 x^5+19 x^4+10 x^3+40 x^2+22 x+18$
• $y^2=11 x^6+11 x^5+30 x^4+41 x^3+19 x^2+8 x+41$
• $y^2=36 x^6+2 x^5+8 x^4+29 x^3+37 x+3$
• $y^2=6 x^6+x^5+6 x^4+22 x^3+11 x^2+11 x+24$
• $y^2=13 x^6+6 x^5+4 x^4+34 x^3+12 x^2+10 x+5$
• $y^2=41 x^6+39 x^5+28 x^4+22 x^3+13 x^2+10 x+15$
• $y^2=5 x^6+40 x^5+x^4+2 x^3+7 x^2+24 x+12$
• $y^2=2 x^6+18 x^5+3 x^4+21 x^3+27 x^2+37 x+28$
• $y^2=22 x^6+29 x^5+12 x^4+15 x^3+23 x^2+32 x+27$
• $y^2=9 x^6+36 x^5+5 x^4+29 x^3+29 x^2+13 x+8$
• $y^2=32 x^6+17 x^5+18 x^4+21 x^3+3 x^2+27 x+12$

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 4.0.1761536.1.

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.ae_dk	$2$	(not in LMFDB)