Cremona's table of elliptic curves

6084 = 2² · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	6084m	Isogeny class
Conductor	6084	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-31539456 = -1 · 28 · 36 · 132	Discriminant
Eigenvalues	2- 3- -3  4  0 13+ -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-39,286]	[a1,a2,a3,a4,a6]
Generators	[-1:18:1]	Generators of the group modulo torsion
j	-208	j-invariant
L	3.7171172538456	L(r)(E,1)/r!
Ω	1.808307109592	Real period
R	0.34259642016637	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	24336ca1 97344cn1 676b1 6084l1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6084m1

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
-	-	-3	4	0	+	-3	-2	6	-9	-2	7	3	-4	-6	-9	0	5	-2	-6	1	-4	12	6	-14

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Quadratic twists for elliptic curve 6084m1

-4	8	-3	13
24336ca1	97344cn1	676b1	6084l1

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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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