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	6006d	Isogeny class
Conductor	6006	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-85584085761174 = -1 · 2 · 3 · 78 · 114 · 132	Discriminant
Eigenvalues	2+ 3+  2 7+ 11- 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-644,-445410]	[a1,a2,a3,a4,a6]
j	-29609739866953/85584085761174	j-invariant
L	1.0991709942648	L(r)(E,1)/r!
Ω	0.27479274856619	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	48048cq3 18018ba4 42042bq3 66066cb3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006d4

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	+	-	+	-2	0	-4	2	0	-2	6	8	-12	2	4	2	-4	12	10	-8	-12	18	2

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Quadratic twists for elliptic curve 6006d4

-4	-3	-7	-11	13
48048cq3	18018ba4	42042bq3	66066cb3	78078ch3

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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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