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	4998p	Isogeny class
Conductor	4998	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	28224	Modular degree for the optimal curve
Δ	-867177304189434 = -1 · 2 · 37 · 79 · 173	Discriminant
Eigenvalues	2+ 3- -1 7-  5 -1 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-11884,-1502980]	[a1,a2,a3,a4,a6]
Generators	[298:4481:1]	Generators of the group modulo torsion
j	-4599141247/21489462	j-invariant
L	3.3024116540658	L(r)(E,1)/r!
Ω	0.20709090967767	Real period
R	1.1390482908503	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39984bq1 14994cw1 124950gc1 4998h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998p1

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	-1	+	-4	-6	-4	10	-3	6	-11	2	-7	-4	-14	-5	-10	1	7	-9	13	13

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Quadratic twists for elliptic curve 4998p1

-4	-3	5	-7	17
39984bq1	14994cw1	124950gc1	4998h1	84966p1

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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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