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

• Label: 2.43.aq_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:	$\pm0.291171725172$, $\pm0.291171725172$
Angle rank:	$1$ (numerical)
Jacobians:	$25$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1296$	$3504384$	$6404480784$	$11710193504256$	$21612468163145616$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$28$	$1894$	$80548$	$3425230$	$147015148$	$6321140278$	$271816540660$	$11688193293214$	$502592645091004$	$21611482878846214$

Jacobians and polarizations

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

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.ai^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.a_w	$2$	(not in LMFDB)
2.43.q_fu	$2$	(not in LMFDB)
2.43.an_ew	$3$	(not in LMFDB)
2.43.ak_eh	$3$	(not in LMFDB)
2.43.f_as	$3$	(not in LMFDB)
2.43.i_v	$3$	(not in LMFDB)
2.43.ba_jv	$3$	(not in LMFDB)