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	2006i	Isogeny class
Conductor	2006	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	34102 = 2 · 172 · 59	Discriminant
Eigenvalues	2-  0  0  2 -6 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-630,6239]	[a1,a2,a3,a4,a6]
Generators	[126:-13:8]	Generators of the group modulo torsion
j	27612067640625/34102	j-invariant
L	4.1929585228454	L(r)(E,1)/r!
Ω	3.11135727657	Real period
R	2.6952600747078	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	16048x2 64192w2 18054b2 50150a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006i2

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

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Quadratic twists for elliptic curve 2006i2

-4	8	-3	5	-7	17	-59
16048x2	64192w2	18054b2	50150a2	98294o2	34102k2	118354g2

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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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