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	6630p	Isogeny class
Conductor	6630	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	-23957190366720 = -1 · 29 · 3 · 5 · 133 · 175	Discriminant
Eigenvalues	2- 3+ 5+  2 -1 13+ 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4161,255423]	[a1,a2,a3,a4,a6]
Generators	[-21:588:1]	Generators of the group modulo torsion
j	-7967524044697489/23957190366720	j-invariant
L	5.107990216224	L(r)(E,1)/r!
Ω	0.59277413684162	Real period
R	0.19149096871646	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	53040cj1 19890o1 33150t1 86190q1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630p1

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	-1	+	-	-1	-4	-4	-5	3	8	-9	-10	10	-6	5	-8	2	-8	-12	17	1	-6

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Quadratic twists for elliptic curve 6630p1

-4	-3	5	13	17
53040cj1	19890o1	33150t1	86190q1	112710cx1

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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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