Cremona's table of elliptic curves

6630 = 2 · 3 · 5 · 13 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	6630k	Isogeny class
Conductor	6630	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	2648775168000 = 212 · 34 · 53 · 13 · 173	Discriminant
Eigenvalues	2+ 3- 5+  2  0 13- 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-166134,-26077304]	[a1,a2,a3,a4,a6]
Generators	[322595:8582211:343]	Generators of the group modulo torsion
j	507102228823216499929/2648775168000	j-invariant
L	3.6812411400349	L(r)(E,1)/r!
Ω	0.23647507589147	Real period
R	7.7835711145397	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	53040bl3 19890bi3 33150bk3 86190cw3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630k3

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

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Quadratic twists for elliptic curve 6630k3

-4	-3	5	13	17
53040bl3	19890bi3	33150bk3	86190cw3	112710q3

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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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