Cremona's table of elliptic curves

9870 = 2 · 3 · 5 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 7- 47-	Signs for the Atkin-Lehner involutions
Class	9870q	Isogeny class
Conductor	9870	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-175350420 = -1 · 22 · 34 · 5 · 72 · 472	Discriminant
Eigenvalues	2- 3+ 5- 7- -2  2  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,45,645]	[a1,a2,a3,a4,a6]
Generators	[-5:20:1]	Generators of the group modulo torsion
j	10063705679/175350420	j-invariant
L	6.2046829286666	L(r)(E,1)/r!
Ω	1.3448404364682	Real period
R	1.1534236256609	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	78960cx2 29610h2 49350s2 69090bo2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870q2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-	-	-2	2	0	-8	8	-6	-8	-2	-10	0	-	-2	-6	-6	8	-8	-14	4	-4	-2	12

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Quadratic twists for elliptic curve 9870q2

-4	-3	5	-7
78960cx2	29610h2	49350s2	69090bo2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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