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	9870f	Isogeny class
Conductor	9870	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	9393772500 = 22 · 35 · 54 · 7 · 472	Discriminant
Eigenvalues	2+ 3- 5+ 7+  2  0 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-36264,2654962]	[a1,a2,a3,a4,a6]
Generators	[98:162:1]	Generators of the group modulo torsion
j	5273920936142579449/9393772500	j-invariant
L	3.5859674451124	L(r)(E,1)/r!
Ω	1.109279252523	Real period
R	0.32327003655359	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	78960br2 29610bd2 49350br2 69090l2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870f2

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	0	-2	-6	6	-8	-2	2	6	8	-	-10	4	10	-8	12	4	0	-12	-14	6

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Quadratic twists for elliptic curve 9870f2

-4	-3	5	-7
78960br2	29610bd2	49350br2	69090l2

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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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