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

• Label: 2.43.at_gm
• 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:	$1 - 19 x + 168 x^{2} - 817 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.107629191891$, $\pm0.331360144677$
Angle rank:	$2$ (numerical)
Number field:	4.0.2639736.2
Galois group:	$D_{4}$
Jacobians:	$12$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1182$	$3373428$	$6342503256$	$11692058561184$	$21610222858697682$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$25$	$1825$	$79774$	$3419929$	$146999875$	$6321274450$	$271818796225$	$11688209594929$	$502592701324282$	$21611482761396625$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

• $y^2=15 x^6+12 x^5+42 x^4+21 x^3+33 x^2+38 x+19$
• $y^2=2 x^6+34 x^5+14 x^4+35 x^3+2 x^2+37 x+12$
• $y^2=37 x^6+9 x^5+3 x^4+18 x^3+20 x^2+24 x+3$
• $y^2=2 x^6+8 x^5+12 x^4+33 x^3+18 x^2+x+29$
• $y^2=26 x^6+37 x^5+20 x^4+4 x^3+34 x^2+23 x+5$
• $y^2=12 x^6+25 x^5+29 x^4+21 x^2+10 x+21$
• $y^2=18 x^6+4 x^5+25 x^4+14 x^3+18 x^2+10 x+23$
• $y^2=7 x^6+39 x^5+6 x^4+16 x^3+16 x^2+24 x+7$
• $y^2=12 x^6+37 x^5+22 x^4+23 x^3+x^2+8 x+18$
• $y^2=15 x^6+19 x^5+19 x^4+42 x^3+13 x^2+17 x+33$
• $y^2=34 x^6+37 x^5+30 x^4+40 x^3+9 x^2+11 x+1$
• $y^2=39 x^6+23 x^5+11 x^4+22 x^3+37 x^2+8 x+32$

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 4.0.2639736.2.

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.t_gm	$2$	(not in LMFDB)