Cremona's table of elliptic curves

6006 = 2 · 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11- 13+	Signs for the Atkin-Lehner involutions
Class	6006h	Isogeny class
Conductor	6006	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	303624334645632 = 27 · 312 · 74 · 11 · 132	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1269821,550229949]	[a1,a2,a3,a4,a6]
Generators	[-625:33482:1]	Generators of the group modulo torsion
j	226439278116330906299737/303624334645632	j-invariant
L	2.2243425251256	L(r)(E,1)/r!
Ω	0.46243571051899	Real period
R	1.2025144655401	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	48048cb4 18018bk3 42042bp4 66066br4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006h4

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	-	-	+	2	4	-4	2	-4	-10	2	8	0	2	-12	2	-4	-12	14	16	8	-6	10

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Quadratic twists for elliptic curve 6006h4

-4	-3	-7	-11	13
48048cb4	18018bk3	42042bp4	66066br4	78078bu4

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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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