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	2006j	Isogeny class
Conductor	2006	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-272816 = -1 · 24 · 172 · 59	Discriminant
Eigenvalues	2- -1 -3  1  4 -2 17-  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-12,-35]	[a1,a2,a3,a4,a6]
Generators	[7:13:1]	Generators of the group modulo torsion
j	-192100033/272816	j-invariant
L	3.2999073540679	L(r)(E,1)/r!
Ω	1.2192159980904	Real period
R	0.33832267613331	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	16048ba1 64192bb1 18054f1 50150c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006j1

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	-3	1	4	-2	-	1	4	-5	-6	-8	-11	2	-8	-9	+	0	-4	8	-10	7	12	-10	-10

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Quadratic twists for elliptic curve 2006j1

-4	8	-3	5	-7	17	-59
16048ba1	64192bb1	18054f1	50150c1	98294p1	34102n1	118354j1

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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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