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	3666b	Isogeny class
Conductor	3666	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	-234624 = -1 · 27 · 3 · 13 · 47	Discriminant
Eigenvalues	2+ 3+ -1  1 -2 13-  6 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-43,-131]	[a1,a2,a3,a4,a6]
j	-9116230969/234624	j-invariant
L	0.92797286932826	L(r)(E,1)/r!
Ω	0.92797286932826	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	29328v1 117312r1 10998q1 91650cz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3666b1

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
+	+	-1	1	-2	-	6	-3	6	0	6	-10	8	-6	+	6	-5	-10	8	16	14	-8	11	5	-10

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Quadratic twists for elliptic curve 3666b1

-4	8	-3	5	13
29328v1	117312r1	10998q1	91650cz1	47658s1

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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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