Cremona's table of elliptic curves

5586 = 2 · 3 · 7² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 19+	Signs for the Atkin-Lehner involutions
Class	5586f	Isogeny class
Conductor	5586	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	42811059312 = 24 · 32 · 77 · 192	Discriminant
Eigenvalues	2+ 3+ -4 7- -2  0 -8 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-29327,1920885]	[a1,a2,a3,a4,a6]
Generators	[-134:1929:1] [734:-19771:1]	Generators of the group modulo torsion
j	23711636464489/363888	j-invariant
L	2.8176693511813	L(r)(E,1)/r!
Ω	1.0446954982844	Real period
R	0.33714002738232	Regulator
r	2	Rank of the group of rational points
S	0.99999999999963	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	44688du2 16758bj2 798f2 106134di2	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586f2

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

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Quadratic twists for elliptic curve 5586f2

-4	-3	-7	-19
44688du2	16758bj2	798f2	106134di2

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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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