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

• Label: 2.43.e_dj
• 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:	$1 + 4 x + 87 x^{2} + 172 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.506503820926$, $\pm0.591849557790$
Angle rank:	$2$ (numerical)
Number field:	4.0.3913488.1
Galois group:	$D_{4}$
Jacobians:	$18$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2113$	$3720993$	$6284645188$	$11670496398249$	$21615381918749113$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$48$	$2008$	$79044$	$3413620$	$147034968$	$6321495454$	$271817523144$	$11688198129700$	$502592643364956$	$21611482316754088$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

• $y^2=17 x^6+40 x^5+16 x^3+16 x^2+32 x+36$
• $y^2=4 x^6+40 x^5+18 x^4+40 x^3+5 x^2+28 x+39$
• $y^2=31 x^6+38 x^5+x^4+27 x^3+24 x^2+11 x+21$
• $y^2=3 x^6+42 x^5+31 x^4+34 x^3+32 x^2+20 x+13$
• $y^2=42 x^6+33 x^5+9 x^4+22 x^3+8 x^2+12 x+14$
• $y^2=10 x^6+33 x^5+41 x^4+28 x^3+10 x^2+13 x+18$
• $y^2=40 x^6+2 x^5+8 x^4+17 x^3+30 x^2+33 x+37$
• $y^2=34 x^6+30 x^5+23 x^4+8 x^3+8 x^2+17 x+6$
• $y^2=34 x^6+39 x^5+x^4+25 x^3+20 x^2+x+35$
• $y^2=35 x^6+27 x^5+26 x^4+12 x^3+38 x^2+15 x+28$
• $y^2=31 x^6+33 x^5+31 x^4+11 x^3+5 x^2+7 x+26$
• $y^2=30 x^6+36 x^5+18 x^4+11 x^3+32 x^2+10 x+6$
• $y^2=36 x^6+37 x^5+32 x^4+7 x^3+40 x^2+42 x+23$
• $y^2=5 x^6+28 x^4+30 x^3+11 x^2+7 x+14$
• $y^2=x^6+15 x^5+14 x^3+21 x^2+6 x+16$
• $y^2=5 x^6+10 x^5+16 x^4+39 x^3+9 x^2+x+37$
• $y^2=16 x^6+4 x^5+10 x^4+5 x^3+24 x^2+40 x+39$
• $y^2=5 x^6+25 x^5+7 x^4+13 x^3+40 x^2+36 x+1$

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 4.0.3913488.1.

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.ae_dj	$2$	(not in LMFDB)