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

• Label: 2.47.n_el
• 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:	$1 + 13 x + 115 x^{2} + 611 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.544022090874$, $\pm0.800675976909$
Angle rank:	$2$ (numerical)
Number field:	4.0.86042525.1
Galois group:	$D_{4}$
Jacobians:	$42$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2949$	$5016249$	$10732233771$	$23810272974621$	$52596615736119984$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$61$	$2271$	$103369$	$4879475$	$229334036$	$10779525027$	$506621487755$	$23811279432979$	$1119130589850763$	$52599131862880686$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=37 x^6+43 x^5+15 x^3+38 x^2+15 x+21$
• $y^2=22 x^6+31 x^5+36 x^4+41 x^3+3 x^2+10 x+9$
• $y^2=24 x^6+34 x^5+39 x^4+16 x^3+31 x^2+17 x+33$
• $y^2=21 x^6+21 x^5+33 x^4+25 x^3+11 x^2+33 x+17$
• $y^2=24 x^6+16 x^5+5 x^4+38 x^3+24 x^2+44 x+17$
• $y^2=15 x^6+5 x^5+35 x^4+35 x^3+4 x^2+31 x+42$
• $y^2=40 x^6+10 x^5+35 x^4+29 x^3+22 x^2+28 x+1$
• $y^2=24 x^6+37 x^5+42 x^4+33 x^3+41 x^2+38 x+21$
• $y^2=12 x^6+19 x^5+2 x^4+6 x^3+20 x^2+45 x+36$
• $y^2=2 x^6+8 x^5+44 x^4+43 x^3+8 x^2+28 x+14$
• $y^2=6 x^6+x^5+45 x^4+31 x^3+31 x^2+14 x+7$
• $y^2=x^6+35 x^5+44 x^4+9 x^3+18 x^2+46 x+45$
• $y^2=24 x^6+32 x^5+23 x^4+10 x^3+41 x^2+3 x+33$
• $y^2=34 x^6+27 x^5+15 x^4+8 x^3+27 x^2+38 x+45$
• $y^2=10 x^6+x^5+41 x^4+30 x^3+13 x^2+41 x+32$
• $y^2=45 x^6+25 x^5+22 x^4+18 x^3+40 x^2+15 x+16$
• $y^2=17 x^6+19 x^5+4 x^4+7 x^3+3 x^2+37 x+39$
• $y^2=21 x^6+35 x^5+46 x^4+34 x^3+12 x^2+45 x+21$
• $y^2=14 x^6+22 x^5+45 x^4+23 x^3+12 x^2+23 x+16$
• $y^2=46 x^6+26 x^5+16 x^4+15 x^3+11 x^2+31 x+13$
• and

• $y^2=27 x^6+33 x^5+32 x^4+37 x^3+21 x^2+23 x+31$
• $y^2=34 x^6+16 x^5+44 x^4+31 x^3+10 x^2+19 x+6$
• $y^2=21 x^6+5 x^5+20 x^4+7 x^3+35 x^2+15 x+25$
• $y^2=16 x^6+25 x^5+35 x^4+27 x^3+39 x^2+41 x+16$
• $y^2=24 x^6+28 x^5+46 x^4+x^3+45 x^2+20 x+8$
• $y^2=40 x^6+3 x^5+15 x^4+40 x^3+15 x^2+42 x+17$
• $y^2=26 x^6+7 x^5+30 x^4+9 x^3+24 x^2+31 x+23$
• $y^2=19 x^6+9 x^5+30 x^4+11 x^3+7 x^2+x+16$
• $y^2=18 x^6+45 x^5+42 x^4+7 x^3+22 x^2+21 x+34$
• $y^2=31 x^6+18 x^5+31 x^4+4 x^3+37 x^2+4 x+3$
• $y^2=6 x^6+29 x^5+34 x^4+16 x^3+13 x^2+28 x+39$
• $y^2=33 x^6+24 x^5+21 x^4+30 x^3+28 x^2+18 x+37$
• $y^2=44 x^6+30 x^5+45 x^4+21 x^3+19 x^2+34 x+36$
• $y^2=16 x^6+46 x^5+43 x^4+35 x^3+42 x^2+44 x+28$
• $y^2=13 x^6+29 x^5+29 x^4+42 x^3+46 x^2+42 x+29$
• $y^2=16 x^6+43 x^5+5 x^4+44 x^3+11 x^2+16 x+3$
• $y^2=36 x^6+25 x^5+25 x^4+5 x^3+29 x^2+12 x+5$
• $y^2=17 x^6+45 x^5+30 x^4+21 x^3+16 x^2+39 x+1$
• $y^2=18 x^6+30 x^5+29 x^4+46 x^3+2 x^2+3 x+5$
• $y^2=6 x^6+26 x^5+24 x^4+28 x^3+2 x^2+3$
• $y^2=3 x^6+13 x^5+40 x^3+41 x+1$
• $y^2=4 x^6+8 x^5+4 x^4+15 x^3+20 x^2+36 x+5$

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 4.0.86042525.1.

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.an_el	$2$	(not in LMFDB)