Cremona's table of elliptic curves

1584 = 2⁴ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	1584l	Isogeny class
Conductor	1584	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-380869401673728 = -1 · 215 · 38 · 116	Discriminant
Eigenvalues	2- 3-  0 -2 11+ -4  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5835,-954502]	[a1,a2,a3,a4,a6]
Generators	[127:594:1]	Generators of the group modulo torsion
j	-7357983625/127552392	j-invariant
L	2.7139294909586	L(r)(E,1)/r!
Ω	0.23010048373411	Real period
R	2.9486351429128	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	198b4 6336ce4 528g4 39600df4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584l4

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	-2	+	-4	6	4	6	-6	-8	-10	-6	-8	-6	0	0	8	4	6	2	-14	-12	6	14

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Quadratic twists for elliptic curve 1584l4

-4	8	-3	5	-7	-11
198b4	6336ce4	528g4	39600df4	77616ex4	17424bm4

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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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