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	4998bc	Isogeny class
Conductor	4998	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	9408	Modular degree for the optimal curve
Δ	-2370855118464 = -1 · 27 · 33 · 79 · 17	Discriminant
Eigenvalues	2- 3+ -1 7- -5  5 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,2694,-49785]	[a1,a2,a3,a4,a6]
Generators	[69:651:1]	Generators of the group modulo torsion
j	53582633/58752	j-invariant
L	4.4893243947659	L(r)(E,1)/r!
Ω	0.44143291336133	Real period
R	0.72642075045068	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	39984dc1 14994bc1 124950dh1 4998bp1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998bc1

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	5	+	4	-6	0	2	1	-2	1	6	-9	-4	-6	-1	-6	7	-1	-1	-7	3

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Quadratic twists for elliptic curve 4998bc1

-4	-3	5	-7	17
39984dc1	14994bc1	124950dh1	4998bp1	84966dq1

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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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