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	1584k	Isogeny class
Conductor	1584	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	1216512 = 212 · 33 · 11	Discriminant
Eigenvalues	2- 3+ -4  2 11- -2  2  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-27,10]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1]	Generators of the group modulo torsion
j	19683/11	j-invariant
L	2.451544044269	L(r)(E,1)/r!
Ω	2.363023572512	Real period
R	0.51873034039665	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	99a1 6336bn1 1584i1 39600cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584k1

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

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Quadratic twists for elliptic curve 1584k1

-4	8	-3	5	-7	-11
99a1	6336bn1	1584i1	39600cf1	77616eb1	17424bi1

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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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