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

• Label: 2.43.am_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:	$\pm0.348746511119$, $\pm0.348746511119$
Angle rank:	$1$ (numerical)
Jacobians:	$26$
Cyclic group of points:	no
Non-cyclic primes:	$2, 19$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1444$	$3610000$	$6410564356$	$11696400000000$	$21606541641923044$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$32$	$1950$	$80624$	$3421198$	$146974832$	$6321058350$	$271818228224$	$11688211082398$	$502592693229632$	$21611482336434750$

Jacobians and polarizations

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

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.ag^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.a_by	$2$	(not in LMFDB)
2.43.m_es	$2$	(not in LMFDB)
2.43.g_ah	$3$	(not in LMFDB)