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	6630c	Isogeny class
Conductor	6630	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	12214946250 = 2 · 32 · 54 · 13 · 174	Discriminant
Eigenvalues	2+ 3+ 5+ -4 -4 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1398,-19998]	[a1,a2,a3,a4,a6]
Generators	[-23:37:1] [-21:36:1]	Generators of the group modulo torsion
j	302503589987689/12214946250	j-invariant
L	3.1240763232711	L(r)(E,1)/r!
Ω	0.78264081499612	Real period
R	0.99792786914828	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	53040cl4 19890bd3 33150cb4 86190ce4	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630c3

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

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Quadratic twists for elliptic curve 6630c3

-4	-3	5	13	17
53040cl4	19890bd3	33150cb4	86190ce4	112710bl4

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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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