Cremona's table of elliptic curves

3486 = 2 · 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 83-	Signs for the Atkin-Lehner involutions
Class	3486m	Isogeny class
Conductor	3486	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	430541888112 = 24 · 34 · 7 · 834	Discriminant
Eigenvalues	2- 3- -2 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1889,-1575]	[a1,a2,a3,a4,a6]
j	745476495651217/430541888112	j-invariant
L	3.1634051063673	L(r)(E,1)/r!
Ω	0.79085127659183	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	27888x3 111552d3 10458f3 87150i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3486m4

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

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Quadratic twists for elliptic curve 3486m4

-4	8	-3	5	-7
27888x3	111552d3	10458f3	87150i3	24402s3

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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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