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	4998s	Isogeny class
Conductor	4998	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	13104	Modular degree for the optimal curve
Δ	-4408308735894 = -1 · 2 · 33 · 710 · 172	Discriminant
Eigenvalues	2+ 3- -1 7- -1 -2 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-20459,-1132540]	[a1,a2,a3,a4,a6]
j	-3352478521/15606	j-invariant
L	1.1972402459404	L(r)(E,1)/r!
Ω	0.19954004099006	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	39984cc1 14994cf1 124950ex1 4998a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4998s1

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	-	-1	-2	-	-6	-6	3	5	-4	6	6	2	5	3	12	16	-14	10	15	-1	2	15

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Quadratic twists for elliptic curve 4998s1

-4	-3	5	-7	17
39984cc1	14994cf1	124950ex1	4998a1	84966i1

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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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