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	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	296406297 = 39 · 11 · 372	Discriminant
Eigenvalues	-1 3+  0  2 11+  6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-8480,-298430]	[a1,a2,a3,a4,a6]
Generators	[622:15011:1]	Generators of the group modulo torsion
j	3425878546875/15059	j-invariant
L	2.4212325725093	L(r)(E,1)/r!
Ω	0.49751331387178	Real period
R	4.8666689011127	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	58608x1 3663b1 91575f1 40293a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3663a1

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 3663a1

-4	-3	5	-11
58608x1	3663b1	91575f1	40293a1

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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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