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	1584n	Isogeny class
Conductor	1584	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-7082282262528 = -1 · 213 · 310 · 114	Discriminant
Eigenvalues	2- 3- -2  4 11+ -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1731,-131006]	[a1,a2,a3,a4,a6]
Generators	[89:648:1]	Generators of the group modulo torsion
j	-192100033/2371842	j-invariant
L	2.7345658760368	L(r)(E,1)/r!
Ω	0.31817557698225	Real period
R	1.0743148099129	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	198a4 6336ci4 528j4 39600do3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584n4

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

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Quadratic twists for elliptic curve 1584n4

-4	8	-3	5	-7	-11
198a4	6336ci4	528j4	39600do3	77616fh3	17424bz4

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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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