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

• Label: 2.47.au_hh
• 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:	$1 - 20 x + 189 x^{2} - 940 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.149015098474$, $\pm0.308396401021$
Angle rank:	$2$ (numerical)
Number field:	4.0.122225.1
Galois group:	$D_{4}$
Jacobians:	$10$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1439$	$4833601$	$10833344576$	$23833717988441$	$52603054410179239$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$28$	$2188$	$104344$	$4884276$	$229362108$	$10779226462$	$506623280884$	$23811293692068$	$1119130556079688$	$52599132692844828$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):

• $y^2=22 x^6+40 x^5+16 x^4+13 x^3+6 x^2+19 x+38$
• $y^2=5 x^6+15 x^5+23 x^4+37 x^3+6 x^2+16 x+43$
• $y^2=40 x^6+36 x^5+x^4+8 x^3+45 x^2+21 x+5$
• $y^2=43 x^6+17 x^5+32 x^4+15 x^3+36 x^2+15 x+41$
• $y^2=22 x^6+41 x^5+23 x^4+20 x^3+46 x^2+41 x+16$
• $y^2=43 x^6+8 x^5+24 x^4+25 x^3+42 x^2+29 x+41$
• $y^2=10 x^6+28 x^5+17 x^4+25 x^3+28 x^2+10 x+11$
• $y^2=38 x^6+28 x^5+3 x^4+44 x^3+15 x^2+45 x+9$
• $y^2=35 x^6+46 x^5+30 x^4+33 x^3+14 x^2+7 x+38$
• $y^2=30 x^6+40 x^5+24 x^4+7 x^3+44 x^2+8 x+45$

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 4.0.122225.1.

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.u_hh	$2$	(not in LMFDB)