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

• Label: 2.43.m_es
• 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:	$( 1 + 6 x + 43 x^{2} )^{2}$
	$1 + 12 x + 122 x^{2} + 516 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.651253488881$, $\pm0.651253488881$
Angle rank:	$1$ (numerical)
Jacobians:	$26$
Cyclic group of points:	no
Non-cyclic primes:	$2, 5$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2500$	$3610000$	$6233102500$	$11696400000000$	$21616424137562500$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$56$	$1950$	$78392$	$3421198$	$147042056$	$6321058350$	$271818993992$	$11688211082398$	$502592530644056$	$21611482336434750$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.g^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-34}) \)$)$

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.am_es	$2$	(not in LMFDB)
2.43.a_by	$2$	(not in LMFDB)
2.43.ag_ah	$3$	(not in LMFDB)