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	6006q	Isogeny class
Conductor	6006	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	10368	Modular degree for the optimal curve
Δ	278574424128 = 26 · 33 · 7 · 116 · 13	Discriminant
Eigenvalues	2+ 3-  0 7- 11- 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-3601,78884]	[a1,a2,a3,a4,a6]
Generators	[12:187:1]	Generators of the group modulo torsion
j	5162020164015625/278574424128	j-invariant
L	3.7537276772843	L(r)(E,1)/r!
Ω	0.96309777031297	Real period
R	3.8975561910651	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	48048bd1 18018bn1 42042q1 66066ck1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006q1

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	-4	-6	-6	-4	-4	0	-4	-6	-12	-12	-10	-4	12	-10	8	6	18	14

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Quadratic twists for elliptic curve 6006q1

-4	-3	-7	-11	13
48048bd1	18018bn1	42042q1	66066ck1	78078cs1

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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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