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	6084h	Isogeny class
Conductor	6084	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	32760	Modular degree for the optimal curve
Δ	1607981448926736 = 24 · 36 · 1310	Discriminant
Eigenvalues	2- 3-  2 -1 -5 13+ -3  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-257049,-50124555]	[a1,a2,a3,a4,a6]
Generators	[-2376557415988:1073025650575:8254655261]	Generators of the group modulo torsion
j	1168128	j-invariant
L	4.2177759810496	L(r)(E,1)/r!
Ω	0.21204004821788	Real period
R	19.89141210115	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	24336bq1 97344cc1 676e1 6084k1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6084h1

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
-	-	2	-1	-5	+	-3	3	1	1	8	-3	3	1	4	6	5	-5	-7	-11	-14	-4	12	-9	1

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Quadratic twists for elliptic curve 6084h1

-4	8	-3	13
24336bq1	97344cc1	676e1	6084k1

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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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