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	6630r	Isogeny class
Conductor	6630	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	113629394531250 = 2 · 34 · 512 · 132 · 17	Discriminant
Eigenvalues	2- 3+ 5-  4  4 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-33575,-2325733]	[a1,a2,a3,a4,a6]
j	4185743240664514801/113629394531250	j-invariant
L	4.2393237971145	L(r)(E,1)/r!
Ω	0.35327698309287	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53040cu3 19890b4 33150u3 86190i3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630r3

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

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Quadratic twists for elliptic curve 6630r3

-4	-3	5	13	17
53040cu3	19890b4	33150u3	86190i3	112710cp3

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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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