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

• Label: 2.343.acr_cud
• 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:	$1 - 69 x + 1875 x^{2} - 23667 x^{3} + 117649 x^{4}$
Frobenius angles:	$\pm0.0885013930197$, $\pm0.142666645498$
Angle rank:	$2$ (numerical)
Number field:	4.0.665725.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$95789$	$13722827929$	$1627954277111579$	$191580506576164759741$	$22539349424988989118770864$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$275$	$116639$	$40342223$	$13841234835$	$4747563433940$	$1628413678348643$	$558545866126090901$	$191581231422394616659$	$65712362364267537679229$	$22539340290703308616638014$

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 4.0.665725.1.

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.cr_cud	$2$	(not in LMFDB)