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	1584s	Isogeny class
Conductor	1584	Conductor
∏ cp	80	Product of Tamagawa factors cp
Δ	5770748510208 = 214 · 37 · 115	Discriminant
Eigenvalues	2- 3-  4  2 11-  4  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1449363,-671604910]	[a1,a2,a3,a4,a6]
j	112763292123580561/1932612	j-invariant
L	2.7519165382569	L(r)(E,1)/r!
Ω	0.13759582691284	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	198e3 6336cd3 528f3 39600dz3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584s3

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

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Quadratic twists for elliptic curve 1584s3

-4	8	-3	5	-7	-11
198e3	6336cd3	528f3	39600dz3	77616gw3	17424cf3

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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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