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	6006bf	Isogeny class
Conductor	6006	Conductor
∏ cp	1920	Product of Tamagawa factors cp
Δ	36367448083110144 = 28 · 310 · 76 · 112 · 132	Discriminant
Eigenvalues	2- 3- -2 7- 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-187779,29930049]	[a1,a2,a3,a4,a6]
Generators	[-186:7737:1]	Generators of the group modulo torsion
j	732259344458458209457/36367448083110144	j-invariant
L	6.3451233385098	L(r)(E,1)/r!
Ω	0.36145282692232	Real period
R	0.14628749281377	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	48048bc2 18018k2 42042co2 66066x2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bf2

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	-6	0	-10	-2	-4	0	-2	4	10	-8	16	-10	-8	8	-6	6

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Quadratic twists for elliptic curve 6006bf2

-4	-3	-7	-11	13
48048bc2	18018k2	42042co2	66066x2	78078z2

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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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