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	9870g	Isogeny class
Conductor	9870	Conductor
∏ cp	320	Product of Tamagawa factors cp
Δ	1252738470564000000 = 28 · 310 · 56 · 74 · 472	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2985014,1984052936]	[a1,a2,a3,a4,a6]
Generators	[-987:63493:1]	Generators of the group modulo torsion
j	2941457786004454111199449/1252738470564000000	j-invariant
L	3.7287575592153	L(r)(E,1)/r!
Ω	0.26815618667402	Real period
R	0.6952585367251	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	78960bk2 29610bi2 49350bp2 69090m2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 9870g2

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

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Quadratic twists for elliptic curve 9870g2

-4	-3	5	-7
78960bk2	29610bi2	49350bp2	69090m2

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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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