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	5586r	Isogeny class
Conductor	5586	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	-5015774288322 = -1 · 2 · 310 · 76 · 192	Discriminant
Eigenvalues	2+ 3-  0 7-  4  0  2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4191,149692]	[a1,a2,a3,a4,a6]
Generators	[32:204:1]	Generators of the group modulo torsion
j	-69173457625/42633378	j-invariant
L	3.651426284784	L(r)(E,1)/r!
Ω	0.71047180041693	Real period
R	0.51394387259863	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	44688cj2 16758bb2 114b2 106134ce2	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586r2

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

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Quadratic twists for elliptic curve 5586r2

-4	-3	-7	-19
44688cj2	16758bb2	114b2	106134ce2

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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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