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

• Label: 2.43.at_go
• 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:	$( 1 - 12 x + 43 x^{2} )( 1 - 7 x + 43 x^{2} )$
	$1 - 19 x + 170 x^{2} - 817 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.132197172840$, $\pm0.320784221581$
Angle rank:	$2$ (numerical)
Jacobians:	$12$
Isomorphism classes:	52
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1184$	$3381504$	$6351634304$	$11697312162816$	$21612066286468064$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$25$	$1829$	$79888$	$3421465$	$147012415$	$6321335078$	$271818877621$	$11688208417009$	$502592691082864$	$21611482702820789$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.am $\times$ 1.43.ah 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.am : \(\Q(\sqrt{-7}) \).
• 1.43.ah : \(\Q(\sqrt{-123}) \).

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.43.af_c	$2$	(not in LMFDB)
2.43.f_c	$2$	(not in LMFDB)
2.43.t_go	$2$	(not in LMFDB)