Cremona's table of elliptic curves

2006 = 2 · 17 · 59

Field	Data	Notes
Atkin-Lehner	2+ 17- 59+	Signs for the Atkin-Lehner involutions
Class	2006f	Isogeny class
Conductor	2006	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-128384 = -1 · 27 · 17 · 59	Discriminant
Eigenvalues	2+  3  2  4 -2  1 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-31,77]	[a1,a2,a3,a4,a6]
j	-3354790473/128384	j-invariant
L	3.271858307634	L(r)(E,1)/r!
Ω	3.271858307634	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048bg1 64192bi1 18054o1 50150bd1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006f1

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
+	3	2	4	-2	1	-	0	-1	-3	-7	6	-6	4	-4	4	+	-8	-11	-14	2	10	-1	-4	17

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Quadratic twists for elliptic curve 2006f1

-4	8	-3	5	-7	17	-59
16048bg1	64192bi1	18054o1	50150bd1	98294f1	34102g1	118354v1

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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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