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	6006a	Isogeny class
Conductor	6006	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	-20061784190448 = -1 · 24 · 32 · 78 · 11 · 133	Discriminant
Eigenvalues	2+ 3+  0 7+ 11+ 13+ -4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9100,-401408]	[a1,a2,a3,a4,a6]
Generators	[139:952:1]	Generators of the group modulo torsion
j	-83353234419015625/20061784190448	j-invariant
L	2.2840537931142	L(r)(E,1)/r!
Ω	0.24133146518892	Real period
R	4.7321922802858	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	48048cw1 18018bd1 42042bd1 66066by1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006a1

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

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Quadratic twists for elliptic curve 6006a1

-4	-3	-7	-11	13
48048cw1	18018bd1	42042bd1	66066by1	78078cn1

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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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