Abelian variety isogeny class 2.47.az_jp over $\F_{47}$

• Label: 2.47.az_jp
• Base field: $\F_{47}$
• 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:	$\F_{47}$
Dimension:	$2$
L-polynomial:	$1 - 25 x + 249 x^{2} - 1175 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.0371496985721$, $\pm0.188274597858$
Angle rank:	$2$ (numerical)
Number field:	4.0.3725.1
Galois group:	$D_{4}$
Jacobians:	$1$
Isomorphism classes:	1

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1259$	$4606681$	$10730027681$	$23807424148301$	$52600163994438064$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$23$	$2083$	$103349$	$4878891$	$229349508$	$10779247207$	$506622916739$	$23811280666083$	$1119130401453293$	$52599131627724078$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is hyperelliptic):

• $y^2=35 x^6+35 x^5+32 x^4+40 x^3+43 x^2+13 x+22$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{47}$.

Endomorphism algebra over $\F_{47}$

The endomorphism algebra of this simple isogeny class is 4.0.3725.1.

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
2.47.z_jp	$2$	(not in LMFDB)