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

• Label: 2.47.d_ag
• 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:	$1 + 3 x - 6 x^{2} + 141 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.283838814022$, $\pm0.821523582883$
Angle rank:	$2$ (numerical)
Number field:	4.0.253096153.1
Galois group:	$D_{4}$
Jacobians:	$40$
Isomorphism classes:	40
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2348$	$4836880$	$10831709072$	$23844367336000$	$52594323800387828$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$51$	$2189$	$104328$	$4886457$	$229324041$	$10779294206$	$506620689423$	$23811282418513$	$1119130506440856$	$52599132278895989$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 40 curves (of which all are hyperelliptic):

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

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

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 4.0.253096153.1.

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.ad_ag	$2$	(not in LMFDB)