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

• Label: 2.43.q_fu
• Base field: $\F_{43}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$( 1 + 8 x + 43 x^{2} )^{2}$
	$1 + 16 x + 150 x^{2} + 688 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.708828274828$, $\pm0.708828274828$
Angle rank:	$1$ (numerical)
Jacobians:	$25$
Cyclic group of points:	no
Non-cyclic primes:	$2, 13$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2704$	$3504384$	$6239104144$	$11710193504256$	$21610497073928464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$60$	$1894$	$78468$	$3425230$	$147001740$	$6321140278$	$271820681556$	$11688193293214$	$502592578782684$	$21611482878846214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 25 curves (of which all are hyperelliptic):

• $y^2=15 x^6+19 x^5+36 x^4+16 x^3+36 x^2+22 x+6$
• $y^2=3 x^6+5$
• $y^2=3 x^6+29 x^3+20$
• $y^2=32 x^6+21 x^5+23 x^4+36 x^3+4 x^2+6 x+8$
• $y^2=38 x^5+16 x^4+26 x^3+19 x^2+3 x+11$
• $y^2=2 x^6+41 x^5+3 x^4+39 x^3+18 x^2+14 x+2$
• $y^2=3 x^6+2 x^3+20$
• $y^2=35 x^6+5 x^4+5 x^2+35$
• $y^2=9 x^6+21 x^5+22 x^4+41 x^3+22 x^2+3 x+40$
• $y^2=7 x^6+32 x^4+32 x^2+7$
• $y^2=36 x^6+17 x^5+15 x^4+6 x^3+15 x^2+17 x+36$
• $y^2=4 x^6+42 x^5+5 x^4+32 x^3+5 x^2+42 x+4$
• $y^2=3 x^6+28 x^3+12$
• $y^2=15 x^6+11 x^5+15 x^4+22 x^3+3 x^2+9 x+9$
• $y^2=40 x^6+42 x^5+3 x^4+22 x^3+3 x^2+42 x+40$
• $y^2=3 x^6+27 x^3+37$
• $y^2=8 x^6+16 x^5+13 x^4+29 x^3+11 x^2+14 x+39$
• $y^2=36 x^5+19 x^4+30 x^3+19 x^2+36 x$
• $y^2=36 x^6+31 x^5+33 x^4+31 x^3+22 x^2+9 x+25$
• $y^2=4 x^6+18 x^5+26 x^4+5 x^3+26 x^2+18 x+4$
• $y^2=7 x^6+6 x^4+13 x^3+6 x^2+7$
• $y^2=40 x^6+7 x^5+38 x^4+19 x^3+5 x^2+31 x+38$
• $y^2=7 x^6+23 x^5+29 x^4+2 x^3+39 x^2+32 x+4$
• $y^2=18 x^6+x^5+33 x^4+19 x^3+33 x^2+x+18$
• $y^2=38 x^6+6 x^4+6 x^2+38$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{43}$.

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.i^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.43.aq_fu	$2$	(not in LMFDB)
2.43.a_w	$2$	(not in LMFDB)
2.43.aba_jv	$3$	(not in LMFDB)
2.43.ai_v	$3$	(not in LMFDB)
2.43.af_as	$3$	(not in LMFDB)
2.43.k_eh	$3$	(not in LMFDB)
2.43.n_ew	$3$	(not in LMFDB)