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

• Label: 2.43.ap_fi
• 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:	$1 - 15 x + 138 x^{2} - 645 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.239956780558$, $\pm0.363894322130$
Angle rank:	$2$ (numerical)
Number field:	4.0.829141.1
Galois group:	$D_{4}$
Jacobians:	$44$
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1328$	$3516544$	$6393273536$	$11702509851136$	$21611360923889168$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$29$	$1901$	$80408$	$3422985$	$147007619$	$6321259622$	$271818207473$	$11688200229649$	$502592601733544$	$21611482097746061$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 44 curves (of which all are hyperelliptic):

• $y^2=8 x^6+30 x^5+3 x^4+13 x^3+4 x^2+6 x+34$
• $y^2=19 x^6+14 x^5+37 x^4+35 x^3+40 x^2+9 x+37$
• $y^2=19 x^6+7 x^5+27 x^4+8 x^3+28 x^2+6 x+12$
• $y^2=39 x^6+13 x^5+27 x^4+21 x^3+26 x^2+37 x+37$
• $y^2=3 x^5+6 x^4+41 x^3+9 x^2+27 x+12$
• $y^2=6 x^6+29 x^5+16 x^4+5 x^3+21 x^2+2 x+18$
• $y^2=25 x^6+34 x^5+11 x^4+15 x^3+24 x^2+40 x+10$
• $y^2=36 x^6+39 x^5+3 x^4+4 x^3+14 x^2+11 x+18$
• $y^2=26 x^6+29 x^5+16 x^4+42 x^3+2 x^2+5 x+23$
• $y^2=28 x^6+35 x^5+26 x^4+22 x^3+42 x^2+25 x+22$
• $y^2=34 x^6+18 x^5+30 x^4+10 x^3+36 x^2+33 x+9$
• $y^2=18 x^6+6 x^5+21 x^4+31 x^3+30 x^2+39 x+27$
• $y^2=21 x^6+14 x^5+34 x^4+26 x^3+37 x^2+39 x+20$
• $y^2=39 x^6+25 x^5+26 x^4+10 x^3+27 x^2+11 x+9$
• $y^2=3 x^6+26 x^5+38 x^4+35 x^3+13 x^2+13 x+28$
• $y^2=37 x^6+20 x^5+28 x^4+37 x^3+x^2+36 x+27$
• $y^2=19 x^6+25 x^5+6 x^4+34 x^3+30 x^2+2 x+31$
• $y^2=4 x^6+26 x^5+30 x^4+31 x^3+23 x^2+12 x+32$
• $y^2=30 x^6+7 x^5+39 x^4+26 x^3+8 x^2+14 x+39$
• $y^2=9 x^6+10 x^5+14 x^4+16 x^3+12 x^2+12 x$
• and

• $y^2=5 x^6+13 x^5+37 x^4+11 x^3+3 x^2+22 x+19$
• $y^2=39 x^6+14 x^5+12 x^4+3 x^3+18 x^2+27 x+29$
• $y^2=2 x^5+9 x^4+34 x^3+18 x^2+7 x+12$
• $y^2=33 x^6+6 x^5+24 x^4+30 x^3+19 x^2+13 x+22$
• $y^2=41 x^5+11 x^4+10 x^3+2 x^2+24 x+9$
• $y^2=33 x^6+32 x^5+41 x^4+31 x^3+3 x^2+3 x+29$
• $y^2=34 x^6+9 x^5+5 x^4+33 x^3+38 x^2+12 x+11$
• $y^2=26 x^6+39 x^5+7 x^4+5 x^3+5 x^2+38 x+9$
• $y^2=33 x^6+39 x^5+34 x^4+11 x^3+6 x^2+23 x+34$
• $y^2=30 x^6+14 x^5+11 x^4+13 x^3+23 x^2+24 x+14$
• $y^2=3 x^6+17 x^5+40 x^3+4 x^2+16 x+41$
• $y^2=36 x^6+16 x^5+23 x^4+9 x^3+16 x^2+20 x+39$
• $y^2=18 x^6+23 x^4+6 x^3+38 x^2+30 x+12$
• $y^2=27 x^6+2 x^5+21 x^4+32 x^2+33 x$
• $y^2=26 x^6+7 x^5+22 x^4+36 x^3+11 x^2+12 x+25$
• $y^2=34 x^6+24 x^5+24 x^4+34 x^3+19 x^2+27 x+18$
• $y^2=37 x^6+27 x^5+15 x^4+32 x^3+28 x^2+20 x+31$
• $y^2=18 x^6+5 x^5+42 x^4+29 x^3+33 x^2+7 x+40$
• $y^2=30 x^6+24 x^5+17 x^4+5 x^3+35 x^2+16 x+29$
• $y^2=13 x^6+4 x^5+34 x^4+21 x^3+28 x^2+26 x+32$
• $y^2=24 x^6+13 x^5+40 x^4+16 x^3+10 x^2+41 x+35$
• $y^2=29 x^6+2 x^5+39 x^4+23 x^3+6 x^2+23 x+2$
• $y^2=3 x^6+19 x^5+27 x^4+41 x^3+32 x^2+39 x+4$
• $y^2=24 x^6+12 x^5+19 x^3+35 x^2+27 x+2$

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 4.0.829141.1.

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.p_fi	$2$	(not in LMFDB)