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	1584a	Isogeny class
Conductor	1584	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3345408 = 210 · 33 · 112	Discriminant
Eigenvalues	2+ 3+  0  2 11+ -6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,234]	[a1,a2,a3,a4,a6]
Generators	[-5:22:1]	Generators of the group modulo torsion
j	1687500/121	j-invariant
L	2.8755300243878	L(r)(E,1)/r!
Ω	2.4606111694459	Real period
R	0.58431215384496	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	792c2 6336bo2 1584b2 39600a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584a2

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

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Quadratic twists for elliptic curve 1584a2

-4	8	-3	5	-7	-11
792c2	6336bo2	1584b2	39600a2	77616e2	17424e2

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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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