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

• Label: 2.43.as_fz
• 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:	$1 - 18 x + 155 x^{2} - 774 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.100695717907$, $\pm0.361290196300$
Angle rank:	$2$ (numerical)
Number field:	4.0.338832.4
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1213$	$3392761$	$6338516944$	$11686572222921$	$21608595650203573$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$26$	$1836$	$79724$	$3418324$	$146988806$	$6321276726$	$271819331810$	$11688212314468$	$502592686387508$	$21611482505118396$

Jacobians and polarizations

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

• $y^2=4 x^6+12 x^5+35 x^4+23 x^3+x^2+33 x+12$
• $y^2=37 x^6+11 x^5+27 x^4+28 x^3+12 x^2+8 x+5$
• $y^2=36 x^6+31 x^5+12 x^4+9 x^3+22 x^2+39 x+3$
• $y^2=38 x^6+14 x^5+37 x^4+17 x^3+3 x^2+30 x+1$
• $y^2=8 x^6+34 x^5+17 x^3+5 x^2+41 x+5$
• $y^2=36 x^6+27 x^5+6 x^4+5 x^3+36 x^2+28 x+10$
• $y^2=39 x^6+9 x^4+13 x^3+27 x^2+41 x+37$
• $y^2=17 x^6+20 x^5+16 x^4+32 x^3+23 x^2+41 x+26$
• $y^2=36 x^6+27 x^5+12 x^4+32 x^3+3 x+38$
• $y^2=37 x^6+9 x^5+24 x^3+30 x^2+9 x+15$
• $y^2=29 x^6+5 x^5+37 x^4+42 x^3+28 x^2+39 x+8$
• $y^2=2 x^6+23 x^5+37 x^4+13 x^3+38 x^2+8 x+18$

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 4.0.338832.4.

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.s_fz	$2$	(not in LMFDB)