Abelian variety isogeny class 2.343.aco_cqa over $\F_{7^{3}}$

• Label: 2.343.aco_cqa
• Base field: $\F_{7^{3}}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{7^{3}}$
Dimension:	$2$
L-polynomial:	$1 - 66 x + 1768 x^{2} - 22638 x^{3} + 117649 x^{4}$
Frobenius angles:	$\pm0.0876293779317$, $\pm0.194258099826$
Angle rank:	$2$ (numerical)
Number field:	4.0.442176.1
Galois group:	$D_{4}$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$96714$	$13745187108$	$1628197920094050$	$191582247505669571664$	$22539356900488314482946354$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$278$	$116830$	$40348262$	$13841360614$	$4747565008538$	$1628413674474670$	$558545865241860746$	$191581231392231260734$	$65712362363577451051526$	$22539340290691704076015150$

Jacobians and polarizations

This isogeny class contains a Jacobian and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{7^{3}}$.

Endomorphism algebra over $\F_{7^{3}}$

The endomorphism algebra of this simple isogeny class is 4.0.442176.1.

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
2.343.co_cqa	$2$	(not in LMFDB)