Cremona's table of elliptic curves

98568 = 2³ · 3² · 37²

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	98568t	Isogeny class
Conductor	98568	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	5745913504238592 = 210 · 37 · 376	Discriminant
Eigenvalues	2- 3- -2  0 -4  2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-792651,-271601386]	[a1,a2,a3,a4,a6]
Generators	[130018:16549841:8]	Generators of the group modulo torsion
j	28756228/3	j-invariant
L	4.8017305708287	L(r)(E,1)/r!
Ω	0.1600043428113	Real period
R	7.5025004083489	Regulator
r	1	Rank of the group of rational points
S	0.99999999619122	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32856c4 72a3	Quadratic twists by: -3 37

Hecke Eigenvalues for elliptic curve 98568t4

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

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Quadratic twists for elliptic curve 98568t4

-3	37
32856c4	72a3

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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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