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	8	Product of Tamagawa factors cp
Δ	9565584 = 24 · 3 · 74 · 83	Discriminant
Eigenvalues	2- 3- -2 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21249,-1193991]	[a1,a2,a3,a4,a6]
j	1061061310359436177/9565584	j-invariant
L	3.1634051063673	L(r)(E,1)/r!
Ω	0.39542563829591	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27888x4 111552d4 10458f4 87150i4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3486m3

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 3486m3

-4	8	-3	5	-7
27888x4	111552d4	10458f4	87150i4	24402s4

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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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