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

• Label: 2.43.as_fx
• 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:	$1 - 18 x + 153 x^{2} - 774 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0761203202032$, $\pm0.368681889582$
Angle rank:	$2$ (numerical)
Number field:	4.0.4368448.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1211$	$3384745$	$6329882468$	$11681922732025$	$21607034615691371$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$26$	$1832$	$79616$	$3416964$	$146978186$	$6321216494$	$271818980270$	$11688209324356$	$502592660809328$	$21611482365549032$

Jacobians and polarizations

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

• $y^2=34 x^6+40 x^5+24 x^4+36 x^3+5 x^2+13 x+42$
• $y^2=29 x^6+35 x^5+32 x^4+27 x^3+17 x^2+18 x+13$
• $y^2=31 x^6+42 x^5+23 x^4+21 x^3+38 x^2+2 x+19$
• $y^2=34 x^6+7 x^5+32 x^4+28 x^3+19 x^2+41 x+30$
• $y^2=37 x^6+5 x^5+41 x^4+34 x^3+25 x+4$
• $y^2=31 x^6+39 x^5+19 x^4+13 x^3+31 x^2+2 x+10$
• $y^2=36 x^6+2 x^5+33 x^4+30 x^3+10 x^2+15 x+5$
• $y^2=2 x^6+27 x^5+19 x^4+35 x^3+38 x^2+40 x+37$
• $y^2=10 x^6+13 x^5+21 x^4+5 x^3+26 x^2+17 x+14$
• $y^2=24 x^6+29 x^5+31 x^4+2 x^3+23 x^2+38 x+32$
• $y^2=28 x^6+37 x^5+25 x^4+28 x^3+2 x^2+28 x+13$
• $y^2=18 x^6+2 x^5+2 x^4+14 x^3+25 x^2+42 x+16$

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 4.0.4368448.1.

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.s_fx	$2$	(not in LMFDB)