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

• Label: 2.47.ay_jc
• 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:	$1 - 24 x + 236 x^{2} - 1128 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.0663836493035$, $\pm0.219232558220$
Angle rank:	$2$ (numerical)
Number field:	4.0.39168.3
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1294$	$4655812$	$10756836958$	$23816769039504$	$52602264188664574$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$24$	$2106$	$103608$	$4880806$	$229358664$	$10779263898$	$506622808296$	$23811280628734$	$1119130426600344$	$52599132084154266$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which all are hyperelliptic):

• $y^2=23 x^6+23 x^5+3 x^4+8 x^3+41 x^2+45 x+44$
• $y^2=20 x^6+5 x^5+38 x^4+45 x^3+2 x+30$
• $y^2=8 x^6+5 x^5+32 x^3+28 x^2+23 x+17$
• $y^2=36 x^6+4 x^5+31 x^4+3 x^3+37 x^2+42 x+11$

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 4.0.39168.3.

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.y_jc	$2$	(not in LMFDB)