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	8	Product of Tamagawa factors cp
Δ	856424448 = 218 · 33 · 112	Discriminant
Eigenvalues	2- 3+  0 -2 11-  2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-16395,-808006]	[a1,a2,a3,a4,a6]
Generators	[223:2574:1]	Generators of the group modulo torsion
j	4406910829875/7744	j-invariant
L	2.7441828999857	L(r)(E,1)/r!
Ω	0.42191187125549	Real period
R	3.2520806914248	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	198c2 6336bi2 1584h4 39600ce2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584j2

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 1584j2

-4	8	-3	5	-7	-11
198c2	6336bi2	1584h4	39600ce2	77616dq2	17424bc2

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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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