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	4998bq	Isogeny class
Conductor	4998	Conductor
∏ cp	420	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-4041146741821056 = -1 · 27 · 33 · 77 · 175	Discriminant
Eigenvalues	2- 3- -3 7-  1 -1 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-107997,13989681]	[a1,a2,a3,a4,a6]
Generators	[1950:83991:1]	Generators of the group modulo torsion
j	-1184052061112257/34349180544	j-invariant
L	5.6167835386517	L(r)(E,1)/r!
Ω	0.43805883082123	Real period
R	0.03052853452258	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	39984cn1 14994x1 124950k1 714e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998bq1

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
-	-	-3	-	1	-1	-	-6	-2	-2	0	5	-4	-9	0	11	-4	-6	-11	-12	5	-15	-1	-9	9

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Quadratic twists for elliptic curve 4998bq1

-4	-3	5	-7	17
39984cn1	14994x1	124950k1	714e1	84966dc1

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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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