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	4998q	Isogeny class
Conductor	4998	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	119953979208 = 23 · 32 · 78 · 172	Discriminant
Eigenvalues	2+ 3-  2 7- -2 -4 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-18695,-985246]	[a1,a2,a3,a4,a6]
Generators	[228:2458:1]	Generators of the group modulo torsion
j	6141556990297/1019592	j-invariant
L	3.6889465222321	L(r)(E,1)/r!
Ω	0.40829616108908	Real period
R	2.2587443097629	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	39984bt2 14994cz2 124950fs2 714d2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998q2

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	-	-2	-4	+	2	-4	0	0	-8	2	-4	0	-6	10	6	0	-8	6	-12	-6	-6	-14

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Quadratic twists for elliptic curve 4998q2

-4	-3	5	-7	17
39984bt2	14994cz2	124950fs2	714d2	84966w2

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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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