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	6006p	Isogeny class
Conductor	6006	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	58270212 = 22 · 33 · 73 · 112 · 13	Discriminant
Eigenvalues	2+ 3-  0 7- 11+ 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2516,48350]	[a1,a2,a3,a4,a6]
j	1760384222493625/58270212	j-invariant
L	1.8479472707981	L(r)(E,1)/r!
Ω	1.8479472707981	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	48048bl1 18018br1 42042j1 66066cj1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006p1

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

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Quadratic twists for elliptic curve 6006p1

-4	-3	-7	-11	13
48048bl1	18018br1	42042j1	66066cj1	78078cx1

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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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