Cremona's table of elliptic curves

3666 = 2 · 3 · 13 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 47+	Signs for the Atkin-Lehner involutions
Class	3666m	Isogeny class
Conductor	3666	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-2375568 = -1 · 24 · 35 · 13 · 47	Discriminant
Eigenvalues	2- 3-  0 -3 -1 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-48,144]	[a1,a2,a3,a4,a6]
Generators	[6:-12:1]	Generators of the group modulo torsion
j	-12246522625/2375568	j-invariant
L	5.5335087944025	L(r)(E,1)/r!
Ω	2.4785756197189	Real period
R	0.11162678980579	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29328h1 117312k1 10998f1 91650r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3666m1

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	-3	-1	+	-4	-2	-2	3	-4	4	-8	4	+	-4	-10	-13	8	-6	-1	-8	18	9	2

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Quadratic twists for elliptic curve 3666m1

-4	8	-3	5	13
29328h1	117312k1	10998f1	91650r1	47658k1

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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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