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	6006j	Isogeny class
Conductor	6006	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	-663548801916 = -1 · 22 · 3 · 74 · 116 · 13	Discriminant
Eigenvalues	2+ 3- -2 7+ 11+ 13+ -4 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,1063,-36760]	[a1,a2,a3,a4,a6]
j	133018079080823/663548801916	j-invariant
L	0.91446248153894	L(r)(E,1)/r!
Ω	0.45723124076947	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48048bu1 18018bf1 42042m1 66066cy1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006j1

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

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Quadratic twists for elliptic curve 6006j1

-4	-3	-7	-11	13
48048bu1	18018bf1	42042m1	66066cy1	78078di1

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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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