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	6630a	Isogeny class
Conductor	6630	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	18240	Modular degree for the optimal curve
Δ	-40685186580480 = -1 · 219 · 35 · 5 · 13 · 173	Discriminant
Eigenvalues	2+ 3+ 5+  0  3 13+ 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,312,307008]	[a1,a2,a3,a4,a6]
Generators	[11:553:1]	Generators of the group modulo torsion
j	3342032927351/40685186580480	j-invariant
L	2.3803295619233	L(r)(E,1)/r!
Ω	0.50859421757436	Real period
R	4.6802135763081	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53040cd1 19890be1 33150cc1 86190bx1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630a1

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
+	+	+	0	3	+	+	-3	2	-4	-3	9	2	-1	12	0	-12	-3	-2	-14	-2	6	-5	15	-4

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Quadratic twists for elliptic curve 6630a1

-4	-3	5	13	17
53040cd1	19890be1	33150cc1	86190bx1	112710bj1

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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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