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

• Label: 2.47.s_gr
• 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:	$1 + 18 x + 173 x^{2} + 846 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.686612703959$, $\pm0.774573251189$
Angle rank:	$2$ (numerical)
Number field:	4.0.664128.3
Galois group:	$D_{4}$
Jacobians:	$12$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3247$	$4932193$	$10678720612$	$23846921341929$	$52594182794134687$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$66$	$2232$	$102852$	$4886980$	$229323426$	$10779114966$	$506624633742$	$23811278922820$	$1119130483189212$	$52599132334581912$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

• $y^2=23 x^6+23 x^5+24 x^4+44 x^3+x^2+29 x+25$
• $y^2=16 x^6+39 x^5+22 x^4+40 x^3+4 x^2+27 x+12$
• $y^2=26 x^6+31 x^5+34 x^4+43 x^3+40 x^2+43 x+21$
• $y^2=38 x^6+14 x^5+26 x^4+13 x^3+39 x^2+6 x+13$
• $y^2=35 x^6+21 x^5+32 x^4+25 x^3+3 x^2+27 x+31$
• $y^2=24 x^6+38 x^5+44 x^4+6 x^3+9 x^2+17 x+16$
• $y^2=19 x^6+x^5+29 x^4+29 x^3+29 x^2+29 x+32$
• $y^2=14 x^6+2 x^5+18 x^4+25 x^3+38 x^2+15 x+1$
• $y^2=10 x^6+9 x^5+17 x^4+41 x^3+22 x^2+33 x+45$
• $y^2=21 x^6+14 x^5+17 x^4+24 x^3+x^2+11 x+18$
• $y^2=18 x^6+22 x^5+2 x^4+8 x^3+9 x^2+22 x+25$
• $y^2=x^6+45 x^5+28 x^4+3 x^3+20 x^2+10 x+16$

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 4.0.664128.3.

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.as_gr	$2$	(not in LMFDB)