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

• Label: 2.43.av_hm
• 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:	$( 1 - 12 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$
	$1 - 21 x + 194 x^{2} - 903 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.132197172840$, $\pm0.259258415261$
Angle rank:	$2$ (numerical)
Jacobians:	$8$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1120$	$3324160$	$6341480320$	$11701907481600$	$21615338661901600$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$23$	$1797$	$79760$	$3422809$	$147034673$	$6321462054$	$271818754139$	$11688200350321$	$502592626619120$	$21611482553603157$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):

• $y^2=15 x^6+41 x^5+10 x^4+14 x^3+21 x+42$
• $y^2=7 x^6+19 x^5+11 x^4+14 x^3+13 x^2+41 x+29$
• $y^2=32 x^6+13 x^5+32 x^4+2 x^3+7 x^2+14 x+5$
• $y^2=3 x^6+34 x^5+27 x^4+34 x^3+33 x^2+9 x+40$
• $y^2=29 x^6+33 x^5+32 x^4+21 x^2+29 x+7$
• $y^2=18 x^6+27 x^5+36 x^4+4 x^3+34 x^2+34 x+6$
• $y^2=34 x^6+28 x^5+2 x^4+29 x^3+42 x^2+23 x+21$
• $y^2=41 x^6+24 x^5+14 x^4+10 x^3+39 x^2+23 x+33$

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.aj 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.aj : \(\Q(\sqrt{-91}) \).

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.ad_aw	$2$	(not in LMFDB)
2.43.d_aw	$2$	(not in LMFDB)
2.43.v_hm	$2$	(not in LMFDB)