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	9870n	Isogeny class
Conductor	9870	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22410910928700 = 22 · 38 · 52 · 7 · 474	Discriminant
Eigenvalues	2- 3+ 5+ 7-  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7461,-101361]	[a1,a2,a3,a4,a6]
Generators	[103:434:1]	Generators of the group modulo torsion
j	45932329342580689/22410910928700	j-invariant
L	5.2638961155345	L(r)(E,1)/r!
Ω	0.53964427789595	Real period
R	2.4385953539886	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	78960ck3 29610l3 49350w3 69090bz3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870n3

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

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Quadratic twists for elliptic curve 9870n3

-4	-3	5	-7
78960ck3	29610l3	49350w3	69090bz3

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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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