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	1584g	Isogeny class
Conductor	1584	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1330255872 = 211 · 310 · 11	Discriminant
Eigenvalues	2+ 3- -2  0 11-  2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4251,106666]	[a1,a2,a3,a4,a6]
Generators	[41:36:1]	Generators of the group modulo torsion
j	5690357426/891	j-invariant
L	2.6021721230692	L(r)(E,1)/r!
Ω	1.4745458805818	Real period
R	0.44118195258233	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	792d3 6336bz3 528d3 39600w4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1584g3

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
+	-	-2	0	-	2	-6	0	4	-2	0	-10	-6	8	-4	6	-12	2	-4	12	-14	-16	-12	-10	-14

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Quadratic twists for elliptic curve 1584g3

-4	8	-3	5	-7	-11
792d3	6336bz3	528d3	39600w4	77616ch4	17424v3

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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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