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	2006k	Isogeny class
Conductor	2006	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-1117454336 = -1 · 216 · 172 · 59	Discriminant
Eigenvalues	2- -3 -3 -1  0  4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,186,-1323]	[a1,a2,a3,a4,a6]
Generators	[41:-293:1]	Generators of the group modulo torsion
j	715236537807/1117454336	j-invariant
L	2.3400239086572	L(r)(E,1)/r!
Ω	0.81716925760361	Real period
R	0.08948665954466	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048be1 64192bf1 18054g1 50150e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006k1

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	-3	-1	0	4	-	-1	-2	7	-4	4	1	-4	2	-1	+	-6	0	-12	-10	-7	4	-12	-8

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Quadratic twists for elliptic curve 2006k1

-4	8	-3	5	-7	17	-59
16048be1	64192bf1	18054g1	50150e1	98294s1	34102q1	118354k1

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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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