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	6084k	Isogeny class
Conductor	6084	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2520	Modular degree for the optimal curve
Δ	333135504 = 24 · 36 · 134	Discriminant
Eigenvalues	2- 3- -2  1  5 13+ -3 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1521,-22815]	[a1,a2,a3,a4,a6]
Generators	[-23:1:1]	Generators of the group modulo torsion
j	1168128	j-invariant
L	3.7797539281868	L(r)(E,1)/r!
Ω	0.76452126630143	Real period
R	1.6479829032846	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	24336bv1 97344bs1 676d1 6084h1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6084k1

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 6084k1

-4	8	-3	13
24336bv1	97344bs1	676d1	6084h1

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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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