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
Δ	-7003834658 = -1 · 2 · 172 · 594	Discriminant
Eigenvalues	2+  0  0  2  4 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1222,-16626]	[a1,a2,a3,a4,a6]
Generators	[4308:26661:64]	Generators of the group modulo torsion
j	-201900421229625/7003834658	j-invariant
L	2.3473584482537	L(r)(E,1)/r!
Ω	0.40290289609367	Real period
R	5.8261146072973	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	16048q2 64192g2 18054u2 50150bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006a2

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 2006a2

-4	8	-3	5	-7	17	-59
16048q2	64192g2	18054u2	50150bg2	98294i2	34102a2	118354m2

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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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