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	4998bd	Isogeny class
Conductor	4998	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	3569242891536 = 24 · 38 · 76 · 172	Discriminant
Eigenvalues	2- 3+  2 7- -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5587,130241]	[a1,a2,a3,a4,a6]
Generators	[13:238:1]	Generators of the group modulo torsion
j	163936758817/30338064	j-invariant
L	5.272399926997	L(r)(E,1)/r!
Ω	0.75100169418891	Real period
R	1.7551225143012	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	39984df2 14994bh2 124950de2 102b2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998bd2

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

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Quadratic twists for elliptic curve 4998bd2

-4	-3	5	-7	17
39984df2	14994bh2	124950de2	102b2	84966dv2

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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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