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

• Label: 2.47.ac_do
• 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:	$1 - 2 x + 92 x^{2} - 94 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.436147703056$, $\pm0.517002742220$
Angle rank:	$2$ (numerical)
Number field:	4.0.4873536.1
Galois group:	$D_{4}$
Jacobians:	$22$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2206$	$5289988$	$10806587350$	$23775258587344$	$52595109320271046$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$2390$	$104086$	$4872294$	$229327466$	$10779486950$	$506624004338$	$23811278111614$	$1119130438968622$	$52599132437250950$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 22 curves (of which all are hyperelliptic):

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

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 4.0.4873536.1.

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.c_do	$2$	(not in LMFDB)