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

• Label: 2.47.aw_ib
• 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:	$1 - 22 x + 209 x^{2} - 1034 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.0623046027155$, $\pm0.285665324434$
Angle rank:	$2$ (numerical)
Number field:	4.0.470592.3
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1363$	$4736425$	$10783679812$	$23815431681625$	$52596806563132603$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$26$	$2144$	$103868$	$4880532$	$229334866$	$10779005846$	$506621413198$	$23811280519588$	$1119130500590756$	$52599132821717264$

Jacobians and polarizations

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

• $y^2=23 x^6+20 x^5+24 x^4+29 x^3+44 x^2+40 x+30$
• $y^2=12 x^6+18 x^5+42 x^4+40 x^3+10 x^2+18 x+9$
• $y^2=23 x^6+46 x^5+3 x^4+44 x^3+9 x^2+2 x+19$
• $y^2=26 x^6+17 x^5+15 x^4+44 x^3+6 x^2+31 x+3$

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 4.0.470592.3.

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.w_ib	$2$	(not in LMFDB)