Cremona's table of elliptic curves

3009 = 3 · 17 · 59

Field	Data	Notes
Atkin-Lehner	3- 17- 59+	Signs for the Atkin-Lehner involutions
Class	3009a	Isogeny class
Conductor	3009	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	728	Modular degree for the optimal curve
Δ	-129420099 = -1 · 37 · 17 · 592	Discriminant
Eigenvalues	0 3- -1  2 -5  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1,-548]	[a1,a2,a3,a4,a6]
Generators	[20:88:1]	Generators of the group modulo torsion
j	-262144/129420099	j-invariant
L	3.2369834602175	L(r)(E,1)/r!
Ω	0.84742363590821	Real period
R	0.27284240668299	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	48144j1 9027b1 75225a1 51153a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 3009a1

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	-	-1	2	-5	1	-	-1	7	-2	-8	8	-3	-9	4	12	+	-14	-4	0	-8	0	-18	-2	-8

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Quadratic twists for elliptic curve 3009a1

-4	-3	5	17
48144j1	9027b1	75225a1	51153a1

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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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