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	5586c	Isogeny class
Conductor	5586	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-301644 = -1 · 22 · 34 · 72 · 19	Discriminant
Eigenvalues	2+ 3+ -1 7- -5 -6 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,17,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1] [1:4:1]	Generators of the group modulo torsion
j	10100279/6156	j-invariant
L	3.1545341396922	L(r)(E,1)/r!
Ω	1.7788627590844	Real period
R	0.4433357946787	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	44688dh1 16758bf1 5586o1 106134cx1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586c1

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
+	+	-1	-	-5	-6	-2	+	-9	-8	-4	-4	4	1	1	-8	6	15	-10	-6	-9	12	-11	-2	8

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Quadratic twists for elliptic curve 5586c1

-4	-3	-7	-19
44688dh1	16758bf1	5586o1	106134cx1

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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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