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	6084j	Isogeny class
Conductor	6084	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	52416	Modular degree for the optimal curve
Δ	-332937792076002048 = -1 · 28 · 313 · 138	Discriminant
Eigenvalues	2- 3- -2  1 -2 13+  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-105456,30731636]	[a1,a2,a3,a4,a6]
Generators	[338:41067:8]	Generators of the group modulo torsion
j	-851968/2187	j-invariant
L	3.5812965560822	L(r)(E,1)/r!
Ω	0.26895144945153	Real period
R	1.1096477832045	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	24336bu1 97344br1 2028a1 6084g1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6084j1

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	-2	+	4	4	-6	-6	-1	10	4	1	10	-8	2	-5	-7	-10	-7	17	-12	16	13

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Quadratic twists for elliptic curve 6084j1

-4	8	-3	13
24336bu1	97344br1	2028a1	6084g1

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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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