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	5586d	Isogeny class
Conductor	5586	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	106464344868 = 22 · 35 · 78 · 19	Discriminant
Eigenvalues	2+ 3+  2 7- -2 -2  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4484,-116388]	[a1,a2,a3,a4,a6]
j	84778086457/904932	j-invariant
L	1.1675636898401	L(r)(E,1)/r!
Ω	0.58378184492004	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	44688dk1 16758bg1 798c1 106134cz1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586d1

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

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Quadratic twists for elliptic curve 5586d1

-4	-3	-7	-19
44688dk1	16758bg1	798c1	106134cz1

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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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