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	5586u	Isogeny class
Conductor	5586	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-99628215367842 = -1 · 2 · 32 · 76 · 196	Discriminant
Eigenvalues	2- 3+  0 7-  0  4 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-20483,1217747]	[a1,a2,a3,a4,a6]
Generators	[230:6349:8]	Generators of the group modulo torsion
j	-8078253774625/846825858	j-invariant
L	5.0120540082583	L(r)(E,1)/r!
Ω	0.58318922040647	Real period
R	4.2971078964431	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	44688dc4 16758g4 114a4 106134bc4	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586u4

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

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Quadratic twists for elliptic curve 5586u4

-4	-3	-7	-19
44688dc4	16758g4	114a4	106134bc4

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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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