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

• Label: 2.43.au_gy
• 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:	$1 - 20 x + 180 x^{2} - 860 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.101829535551$, $\pm0.304721441119$
Angle rank:	$2$ (numerical)
Number field:	4.0.1126656.1
Galois group:	$D_{4}$
Jacobians:	$20$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1150$	$3346500$	$6338837950$	$11694344250000$	$21611320896760750$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$24$	$1810$	$79728$	$3420598$	$147007344$	$6321280930$	$271818304488$	$11688204659998$	$502592686187064$	$21611482897604050$

Jacobians and polarizations

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

• $y^2=37 x^6+39 x^5+34 x^4+3 x^3+6 x^2+19 x+13$
• $y^2=18 x^6+6 x^5+15 x^4+2 x^3+22 x^2+26$
• $y^2=16 x^6+36 x^5+42 x^4+18 x^3+19 x^2+24 x+39$
• $y^2=39 x^6+15 x^5+28 x^4+21 x^3+3 x^2+9 x+27$
• $y^2=22 x^6+x^5+2 x^4+2 x^3+4 x^2+8$
• $y^2=7 x^6+42 x^5+x^4+3 x^3+27 x^2+5 x+33$
• $y^2=29 x^6+29 x^5+40 x^4+31 x^3+39 x^2+13 x+1$
• $y^2=22 x^6+23 x^5+6 x^4+36 x^3+27 x^2+9 x+39$
• $y^2=5 x^6+35 x^5+14 x^4+40 x^3+7 x^2+x+30$
• $y^2=29 x^6+11 x^5+6 x^4+2 x^3+28 x^2+33 x+4$
• $y^2=29 x^6+17 x^5+8 x^4+28 x^3+20 x^2+23 x+31$
• $y^2=18 x^6+18 x^5+35 x^4+10 x^3+17 x^2+14 x$
• $y^2=9 x^6+2 x^5+31 x^4+42 x^3+5 x^2+x+29$
• $y^2=29 x^6+10 x^5+9 x^3+16 x^2+6 x+7$
• $y^2=33 x^6+22 x^5+6 x^4+10 x^3+24 x^2+13 x+1$
• $y^2=42 x^6+11 x^5+4 x^4+5 x^3+10 x^2+17 x+19$
• $y^2=12 x^6+18 x^5+34 x^4+40 x^3+22 x^2+16 x+20$
• $y^2=30 x^6+9 x^5+26 x^4+25 x^3+21 x^2+12 x+12$
• $y^2=30 x^6+21 x^5+12 x^4+18 x^3+42 x^2+5 x+29$
• $y^2=33 x^6+7 x^5+13 x^4+32 x^3+17 x^2+2 x+21$

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 4.0.1126656.1.

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.u_gy	$2$	(not in LMFDB)