Cremona's table of elliptic curves

3663 = 3² · 11 · 37

Field	Data	Notes
Atkin-Lehner	3+ 11+ 37+	Signs for the Atkin-Lehner involutions
Class	3663a	Isogeny class
Conductor	3663	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4463582426523 = 39 · 112 · 374	Discriminant
Eigenvalues	-1 3+  0  2 11+  6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8615,-288332]	[a1,a2,a3,a4,a6]
Generators	[-62:98:1]	Generators of the group modulo torsion
j	3592121380875/226773481	j-invariant
L	2.4212325725093	L(r)(E,1)/r!
Ω	0.49751331387178	Real period
R	2.4333344505564	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	58608x2 3663b2 91575f2 40293a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3663a2

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	+	0	2	+	6	-6	-6	-4	10	8	+	2	-10	-8	-8	-12	-6	16	0	-2	14	4	-4	10

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Quadratic twists for elliptic curve 3663a2

-4	-3	5	-11
58608x2	3663b2	91575f2	40293a2

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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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