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	5586j	Isogeny class
Conductor	5586	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	15360	Modular degree for the optimal curve
Δ	20867011594128 = 24 · 35 · 710 · 19	Discriminant
Eigenvalues	2+ 3+  2 7- -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-7914,155268]	[a1,a2,a3,a4,a6]
Generators	[104:634:1]	Generators of the group modulo torsion
j	466025146777/177366672	j-invariant
L	2.7503315533901	L(r)(E,1)/r!
Ω	0.62184520354848	Real period
R	2.211427810085	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	44688cw1 16758bp1 798d1 106134da1	Quadratic twists by: -4 -3 -7 -19

Hecke Eigenvalues for elliptic curve 5586j1

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

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Quadratic twists for elliptic curve 5586j1

-4	-3	-7	-19
44688cw1	16758bp1	798d1	106134da1

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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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