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	4998k	Isogeny class
Conductor	4998	Conductor
∏ cp	90	Product of Tamagawa factors cp
deg	423360	Modular degree for the optimal curve
Δ	6502343191756430256 = 24 · 315 · 78 · 173	Discriminant
Eigenvalues	2+ 3-  3 7+ -6  5 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13039367,18121613402]	[a1,a2,a3,a4,a6]
j	42531320912955257257/1127938881456	j-invariant
L	2.2058992997878	L(r)(E,1)/r!
Ω	0.22058992997878	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	39984bf1 14994cd1 124950er1 4998j1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998k1

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	+	-6	5	+	-4	0	9	-1	8	-9	8	3	-12	3	8	8	12	2	8	9	6	8

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Quadratic twists for elliptic curve 4998k1

-4	-3	5	-7	17
39984bf1	14994cd1	124950er1	4998j1	84966f1

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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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