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

• Label: 2.47.o_fh
• 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:	$1 + 14 x + 137 x^{2} + 658 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.607682932635$, $\pm0.742026823111$
Angle rank:	$2$ (numerical)
Number field:	\(\Q(\sqrt{-133 -14 \sqrt{6}})\)
Galois group:	$D_{4}$
Jacobians:	$16$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3019$	$5056825$	$10672128772$	$23828088093625$	$52601768227559779$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$62$	$2288$	$102788$	$4883124$	$229356502$	$10779092246$	$506623292650$	$23811285947236$	$1119130515115676$	$52599131904133568$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=2 x^6+3 x^5+30 x^4+31 x^3+46 x^2+40 x+33$
• $y^2=9 x^6+26 x^5+37 x^4+29 x^3+28 x^2+28 x+13$
• $y^2=43 x^6+36 x^5+20 x^4+23 x^3+23 x^2+21 x+21$
• $y^2=16 x^6+25 x^5+8 x^4+16 x^3+x^2+34 x+34$
• $y^2=32 x^6+23 x^5+18 x^4+31 x^3+20 x^2+30 x+42$
• $y^2=x^6+13 x^5+23 x^4+28 x^3+3 x^2+35 x+16$
• $y^2=32 x^6+7 x^5+40 x^4+30 x^3+41 x^2+10 x+19$
• $y^2=29 x^6+46 x^5+21 x^4+28 x^3+20 x^2+13 x+18$
• $y^2=24 x^6+2 x^5+29 x^4+46 x^3+10 x^2+31 x+6$
• $y^2=11 x^6+20 x^5+5 x^4+33 x^3+5 x^2+12 x+9$
• $y^2=37 x^6+33 x^5+8 x^4+9 x^3+46 x^2+39 x+32$
• $y^2=21 x^6+45 x^5+16 x^4+13 x^3+23 x^2+22 x+34$
• $y^2=19 x^6+26 x^5+12 x^4+36 x^3+8 x^2+12 x+23$
• $y^2=25 x^6+21 x^5+27 x^4+42 x^3+45 x^2+19 x+12$
• $y^2=20 x^6+22 x^5+x^4+42 x^3+44 x^2+46 x+42$
• $y^2=37 x^6+10 x^5+22 x^4+44 x^3+29 x^2+4 x+8$

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 \(\Q(\sqrt{-133 -14 \sqrt{6}})\).

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.ao_fh	$2$	(not in LMFDB)