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	9870c	Isogeny class
Conductor	9870	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	784	Modular degree for the optimal curve
Δ	-9870 = -1 · 2 · 3 · 5 · 7 · 47	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0  1  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,-6]	[a1,a2,a3,a4,a6]
j	-1771561/9870	j-invariant
L	1.7010917808644	L(r)(E,1)/r!
Ω	1.7010917808644	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	78960ct1 29610x1 49350ca1 69090p1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870c1

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
+	+	-	-	0	1	6	8	-6	0	-1	11	0	10	-	0	0	-5	4	-2	2	-1	5	13	-1

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Quadratic twists for elliptic curve 9870c1

-4	-3	5	-7
78960ct1	29610x1	49350ca1	69090p1

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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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