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	1584j	Isogeny class
Conductor	1584	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	571304102510592 = 214 · 39 · 116	Discriminant
Eigenvalues	2- 3+  0 -2 11-  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-21195,-296838]	[a1,a2,a3,a4,a6]
Generators	[-17:242:1]	Generators of the group modulo torsion
j	13060888875/7086244	j-invariant
L	2.7441828999857	L(r)(E,1)/r!
Ω	0.42191187125549	Real period
R	1.0840268971416	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	198c4 6336bi4 1584h2 39600ce4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584j4

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

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Quadratic twists for elliptic curve 1584j4

-4	8	-3	5	-7	-11
198c4	6336bi4	1584h2	39600ce4	77616dq4	17424bc4

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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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