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	5586k	Isogeny class
Conductor	5586	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	58736773376064 = 26 · 32 · 710 · 192	Discriminant
Eigenvalues	2+ 3+ -2 7-  0 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-19576,-995840]	[a1,a2,a3,a4,a6]
Generators	[-83:298:1]	Generators of the group modulo torsion
j	7052482298233/499254336	j-invariant
L	2.0082136348085	L(r)(E,1)/r!
Ω	0.40541428735853	Real period
R	2.4767425537627	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	44688cx2 16758bo2 798b2 106134db2	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586k2

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

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Quadratic twists for elliptic curve 5586k2

-4	-3	-7	-19
44688cx2	16758bo2	798b2	106134db2

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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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