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	5586bb	Isogeny class
Conductor	5586	Conductor
∏ cp	480	Product of Tamagawa factors cp
Δ	-260740010604130848 = -1 · 25 · 312 · 76 · 194	Discriminant
Eigenvalues	2- 3- -2 7- -4 -2  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-260289,56689065]	[a1,a2,a3,a4,a6]
Generators	[558:-9513:1]	Generators of the group modulo torsion
j	-16576888679672833/2216253521952	j-invariant
L	5.9441218397789	L(r)(E,1)/r!
Ω	0.30091924166296	Real period
R	0.16461010732011	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	44688cd3 16758n4 114c4 106134q3	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586bb4

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

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Quadratic twists for elliptic curve 5586bb4

-4	-3	-7	-19
44688cd3	16758n4	114c4	106134q3

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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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