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

• Label: 2.47.av_hr
• 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:	$1 - 21 x + 199 x^{2} - 987 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.117269065619$, $\pm0.295691381463$
Angle rank:	$2$ (numerical)
Number field:	4.0.1296981.1
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1401$	$4787217$	$10811952711$	$23827305068109$	$52601463773804976$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$27$	$2167$	$104139$	$4882963$	$229355172$	$10779181747$	$506622935097$	$23811292236211$	$1119130571455533$	$52599133083150382$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which all are hyperelliptic):

• $y^2=26 x^6+14 x^5+35 x^4+17 x^3+10 x^2+16 x+20$
• $y^2=37 x^6+26 x^5+10 x^4+24 x^3+44 x^2+17 x+26$
• $y^2=12 x^6+27 x^5+14 x^4+10 x^3+24 x^2+30 x+5$
• $y^2=34 x^6+38 x^5+3 x^4+37 x^3+10 x^2+45 x+31$
• $y^2=41 x^6+35 x^5+18 x^4+34 x^3+26 x^2+7 x+15$
• $y^2=45 x^6+13 x^5+39 x^4+35 x^3+46 x^2+x+29$
• $y^2=44 x^6+17 x^5+31 x^4+9 x^3+38 x^2+45 x+35$
• $y^2=34 x^6+46 x^5+11 x^4+40 x^3+37 x^2+25 x+5$
• $y^2=2 x^6+45 x^5+44 x^4+36 x^3+30 x^2+30 x+12$
• $y^2=6 x^6+23 x^5+7 x^4+7 x^3+27 x+40$
• $y^2=41 x^6+44 x^5+9 x^4+22 x^3+35 x^2+32 x+11$
• $y^2=20 x^6+22 x^5+21 x^4+24 x^3+46 x^2+41 x+43$
• $y^2=33 x^6+35 x^5+46 x^4+11 x^3+27 x^2+37 x+29$
• $y^2=41 x^6+20 x^5+16 x^4+35 x^3+28 x^2+23 x+9$

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 4.0.1296981.1.

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.v_hr	$2$	(not in LMFDB)