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	1584o	Isogeny class
Conductor	1584	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-2052864 = -1 · 28 · 36 · 11	Discriminant
Eigenvalues	2- 3-  3 -2 11+ -4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,24,-52]	[a1,a2,a3,a4,a6]
Generators	[2:2:1]	Generators of the group modulo torsion
j	8192/11	j-invariant
L	3.0492557716185	L(r)(E,1)/r!
Ω	1.393688252201	Real period
R	1.0939518815642	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	396c1 6336cm1 176c1 39600de1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584o1

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
-	-	3	-2	+	-4	-6	-8	-3	0	-5	-1	0	10	0	6	3	-4	1	15	-4	-2	6	9	-7

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Quadratic twists for elliptic curve 1584o1

-4	8	-3	5	-7	-11
396c1	6336cm1	176c1	39600de1	77616fr1	17424ca1

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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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