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

• Label: 2.43.d_cy
• 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:	$( 1 - 2 x + 43 x^{2} )( 1 + 5 x + 43 x^{2} )$
	$1 + 3 x + 76 x^{2} + 129 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.451268054243$, $\pm0.624505058506$
Angle rank:	$2$ (numerical)
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2058$	$3692052$	$6299924904$	$11677783257504$	$21612316208578998$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$47$	$1993$	$79238$	$3415753$	$147014117$	$6321348178$	$271819117127$	$11688204795601$	$502592551354514$	$21611482113885193$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):

• $y^2=6 x^6+18 x^5+3 x^4+13 x^3+12 x^2+40 x+4$
• $y^2=7 x^6+39 x^5+24 x^4+8 x^3+29 x^2+25 x+9$
• $y^2=4 x^6+35 x^5+25 x^3+17 x^2+24 x+30$
• $y^2=36 x^6+28 x^5+42 x^4+19 x^3+10 x^2+40 x+25$
• $y^2=31 x^6+20 x^5+7 x^4+11 x^3+23 x^2+22 x+40$
• $y^2=13 x^6+20 x^5+17 x^4+8 x^3+27 x^2+11 x+40$
• $y^2=5 x^6+39 x^5+25 x^4+8 x^3+28 x^2+42 x+15$
• $y^2=x^6+27 x^5+30 x^4+29 x^3+x^2+42 x+6$
• $y^2=26 x^6+2 x^5+12 x^4+8 x^3+7 x^2+32 x+40$
• $y^2=25 x^6+21 x^5+6 x^4+10 x^3+42 x^2+10 x+30$
• $y^2=41 x^6+18 x^5+17 x^4+18 x^3+30 x^2+30 x+37$
• $y^2=23 x^6+38 x^5+36 x^4+23 x^3+19 x^2+20 x+18$
• $y^2=33 x^6+22 x^5+15 x^4+11 x^3+x^2+6 x+7$
• $y^2=6 x^6+19 x^5+4 x^4+2 x^3+25 x^2+x+15$
• $y^2=42 x^6+24 x^5+6 x^4+3 x^3+30 x^2+16 x+4$
• $y^2=23 x^6+3 x^5+8 x^4+8 x^3+14 x^2+24 x+38$
• $y^2=8 x^6+2 x^5+32 x^4+12 x^3+15 x^2+x+39$
• $y^2=32 x^6+39 x^5+5 x^4+25 x^3+34 x^2+16 x+27$
• $y^2=26 x^6+35 x^5+37 x^4+29 x^3+41 x^2+25 x+35$
• $y^2=20 x^6+33 x^5+42 x^4+41 x^3+19 x^2+10 x+35$
• $y^2=31 x^6+30 x^5+2 x^4+24 x^3+28 x^2+38 x+4$
• $y^2=3 x^6+28 x^5+8 x^4+22 x^3+31 x+9$
• $y^2=10 x^6+16 x^5+26 x^4+42 x^3+32 x^2+30 x+16$
• $y^2=39 x^6+7 x^5+18 x^4+34 x^3+25 x^2+41 x+20$
• $y^2=24 x^6+18 x^5+2 x^4+39 x^3+34 x^2+32 x+16$
• $y^2=12 x^6+20 x^5+10 x^4+30 x^3+7 x^2+25 x+21$
• $y^2=17 x^6+25 x^4+24 x^3+42 x^2+12 x+1$
• $y^2=42 x^6+16 x^5+13 x^4+40 x^3+6 x^2+42 x+10$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.ac $\times$ 1.43.f and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.43.ac : \(\Q(\sqrt{-42}) \).
• 1.43.f : \(\Q(\sqrt{-3}) \).

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.ah_ds	$2$	(not in LMFDB)
2.43.ad_cy	$2$	(not in LMFDB)
2.43.h_ds	$2$	(not in LMFDB)
2.43.ap_ei	$3$	(not in LMFDB)
2.43.g_cs	$3$	(not in LMFDB)