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	6084b	Isogeny class
Conductor	6084	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-143914537728 = -1 · 28 · 39 · 134	Discriminant
Eigenvalues	2- 3+  0  5  0 13+  0  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,0,-18252]	[a1,a2,a3,a4,a6]
j	0	j-invariant
L	2.8398662606413	L(r)(E,1)/r!
Ω	0.47331104344022	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24336bc2 97344d2 6084b1 6084c2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6084b2

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	5	0	+	0	8	0	0	11	-10	0	5	0	0	0	-1	5	0	-7	17	0	0	-19

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Quadratic twists for elliptic curve 6084b2

-4	8	-3	13
24336bc2	97344d2	6084b1	6084c2

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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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