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

• Label: 2.43.av_hk
• 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:	$1 - 21 x + 192 x^{2} - 903 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0927922568847$, $\pm0.277512598900$
Angle rank:	$2$ (numerical)
Number field:	4.0.413848.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1118$	$3315988$	$6331363688$	$11695118285344$	$21612313035019538$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$23$	$1793$	$79634$	$3420825$	$147014093$	$6321312434$	$271818057359$	$11688199727665$	$502592650556726$	$21611482823443313$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=5x^6+15x^5+14x^3+22x^2+2x+35$
• $y^2=4x^6+29x^5+14x^4+5x^3+33x^2+22x+39$
• $y^2=17x^6+30x^5+6x^4+22x^3+12x^2+32x+1$
• $y^2=28x^6+2x^5+25x^4+5x^2+38x+12$
• $y^2=33x^6+10x^5+4x^4+25x^3+30x^2+7x+28$
• $y^2=20x^6+8x^5+41x^4+12x^3+41x^2+35x+42$

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 4.0.413848.1.

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.v_hk	$2$	(not in LMFDB)