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	3666j	Isogeny class
Conductor	3666	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	528	Modular degree for the optimal curve
Δ	-32994 = -1 · 2 · 33 · 13 · 47	Discriminant
Eigenvalues	2- 3+  3 -5 -2 13+  2  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,6,9]	[a1,a2,a3,a4,a6]
j	23639903/32994	j-invariant
L	2.4943532458264	L(r)(E,1)/r!
Ω	2.4943532458264	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	29328s1 117312bh1 10998h1 91650bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3666j1

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
-	+	3	-5	-2	+	2	5	2	4	2	-6	0	-2	+	14	-3	10	8	12	14	-4	-3	-13	2

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Quadratic twists for elliptic curve 3666j1

-4	8	-3	5	13
29328s1	117312bh1	10998h1	91650bn1	47658f1

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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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