Cremona's table of elliptic curves

4998 = 2 · 3 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4998r	Isogeny class
Conductor	4998	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	-248486805504 = -1 · 214 · 32 · 73 · 173	Discriminant
Eigenvalues	2+ 3-  2 7- -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-180,23986]	[a1,a2,a3,a4,a6]
Generators	[-10:162:1]	Generators of the group modulo torsion
j	-1865409391/724451328	j-invariant
L	3.7281678553787	L(r)(E,1)/r!
Ω	0.80063937832475	Real period
R	2.3282441235775	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	39984bu1 14994da1 124950fy1 4998i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998r1

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	+	-4	6	-10	-8	0	-6	-8	-4	14	14	-14	4	-10	-14	4	6	-2	-2

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Quadratic twists for elliptic curve 4998r1

-4	-3	5	-7	17
39984bu1	14994da1	124950fy1	4998i1	84966z1

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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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