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	6006k	Isogeny class
Conductor	6006	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	-1319205888 = -1 · 210 · 32 · 7 · 112 · 132	Discriminant
Eigenvalues	2+ 3-  0 7+ 11+ 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,104,-1690]	[a1,a2,a3,a4,a6]
Generators	[10:14:1]	Generators of the group modulo torsion
j	126128378375/1319205888	j-invariant
L	3.4458112598347	L(r)(E,1)/r!
Ω	0.7522305060766	Real period
R	1.1451979253696	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	48048bw1 18018bh1 42042g1 66066cs1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006k1

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

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Quadratic twists for elliptic curve 6006k1

-4	-3	-7	-11	13
48048bw1	18018bh1	42042g1	66066cs1	78078df1

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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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