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	6630j	Isogeny class
Conductor	6630	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	8424459021127500 = 22 · 35 · 54 · 138 · 17	Discriminant
Eigenvalues	2+ 3- 5+  0  0 13- 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-103004,11924606]	[a1,a2,a3,a4,a6]
Generators	[771:-20159:1]	Generators of the group modulo torsion
j	120859257477573578809/8424459021127500	j-invariant
L	3.4283123352577	L(r)(E,1)/r!
Ω	0.40541994642305	Real period
R	0.21140501136569	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	53040bk3 19890bg3 33150bj3 86190cu3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6630j4

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

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Quadratic twists for elliptic curve 6630j4

-4	-3	5	13	17
53040bk3	19890bg3	33150bj3	86190cu3	112710o3

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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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