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	1584h	Isogeny class
Conductor	1584	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3632485367808 = 224 · 39 · 11	Discriminant
Eigenvalues	2- 3+  0 -2 11+  2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9315,333666]	[a1,a2,a3,a4,a6]
j	1108717875/45056	j-invariant
L	1.5631168161905	L(r)(E,1)/r!
Ω	0.78155840809524	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	198d3 6336bp3 1584j1 39600bx3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584h3

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 1584h3

-4	8	-3	5	-7	-11
198d3	6336bp3	1584j1	39600bx3	77616dc3	17424bd3

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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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