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	2006a	Isogeny class
Conductor	2006	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	560	Modular degree for the optimal curve
Δ	236708 = 22 · 17 · 592	Discriminant
Eigenvalues	2+  0  0  2  4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1232,-16340]	[a1,a2,a3,a4,a6]
Generators	[180:2270:1]	Generators of the group modulo torsion
j	206896959473625/236708	j-invariant
L	2.3473584482537	L(r)(E,1)/r!
Ω	0.80580579218733	Real period
R	2.9130573036486	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	16048q1 64192g1 18054u1 50150bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006a1

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	4	-2	+	-4	-6	0	-6	8	6	4	-12	2	+	-8	12	-14	-14	-2	-4	14	-10

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Quadratic twists for elliptic curve 2006a1

-4	8	-3	5	-7	17	-59
16048q1	64192g1	18054u1	50150bg1	98294i1	34102a1	118354m1

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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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