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

• Label: 2.47.m_fa
• Base field: $\F_{47}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{47}$
Dimension:	$2$
L-polynomial:	$( 1 + 6 x + 47 x^{2} )^{2}$
	$1 + 12 x + 130 x^{2} + 564 x^{3} + 2209 x^{4}$
Frobenius angles:	$\pm0.644169619151$, $\pm0.644169619151$
Angle rank:	$1$ (numerical)
Jacobians:	$48$
Cyclic group of points:	no
Non-cyclic primes:	$2, 3$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2916$	$5143824$	$10649001636$	$23821583901696$	$52609814292470436$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$60$	$2326$	$102564$	$4881790$	$229391580$	$10778836822$	$506623202628$	$23811303958654$	$1119130365459708$	$52599132068734486$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

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

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{47}$.

Endomorphism algebra over $\F_{47}$

The isogeny class factors as 1.47.g^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-38}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.47.am_fa	$2$	(not in LMFDB)
2.47.a_cg	$2$	(not in LMFDB)
2.47.ag_al	$3$	(not in LMFDB)