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	32	Product of Tamagawa factors cp
Δ	-36713242449000000 = -1 · 26 · 32 · 56 · 132 · 176	Discriminant
Eigenvalues	2+ 3- 5+  2  0 13- 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-163254,-27024248]	[a1,a2,a3,a4,a6]
Generators	[629:10605:1]	Generators of the group modulo torsion
j	-481184224995688814809/36713242449000000	j-invariant
L	3.6812411400349	L(r)(E,1)/r!
Ω	0.11823753794573	Real period
R	3.8917855572699	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	53040bl4 19890bi4 33150bk4 86190cw4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630k4

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 6630k4

-4	-3	5	13	17
53040bl4	19890bi4	33150bk4	86190cw4	112710q4

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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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