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	2006d	Isogeny class
Conductor	2006	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-68204 = -1 · 22 · 172 · 59	Discriminant
Eigenvalues	2+ -1 -1 -5 -2 -4 17- -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-88,284]	[a1,a2,a3,a4,a6]
Generators	[-10:22:1] [2:10:1]	Generators of the group modulo torsion
j	-76711450249/68204	j-invariant
L	2.1115214737215	L(r)(E,1)/r!
Ω	3.451455034549	Real period
R	0.15294429831663	Regulator
r	2	Rank of the group of rational points
S	0.99999999999977	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16048y1 64192y1 18054m1 50150w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006d1

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
+	-1	-1	-5	-2	-4	-	-7	-2	-3	-4	-8	5	4	-8	1	+	14	-10	0	-16	1	-6	-14	2

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Quadratic twists for elliptic curve 2006d1

-4	8	-3	5	-7	17	-59
16048y1	64192y1	18054m1	50150w1	98294c1	34102b1	118354t1

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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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