Cremona's table of elliptic curves

4700 = 2² · 5² · 47

Field	Data	Notes
Atkin-Lehner	2- 5- 47+	Signs for the Atkin-Lehner involutions
Class	4700g	Isogeny class
Conductor	4700	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	8520	Modular degree for the optimal curve
Δ	69031250000 = 24 · 59 · 472	Discriminant
Eigenvalues	2-  0 5-  0  4 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-92000,10740625]	[a1,a2,a3,a4,a6]
Generators	[171:94:1]	Generators of the group modulo torsion
j	2755733225472/2209	j-invariant
L	3.6845836094984	L(r)(E,1)/r!
Ω	0.91377833648958	Real period
R	1.3440836660866	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	18800bn1 75200be1 42300bc1 4700k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4700g1

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
-	0	-	0	4	-4	0	4	0	-6	0	-8	6	8	+	-8	0	2	8	-12	-4	4	0	6	-16

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Quadratic twists for elliptic curve 4700g1

-4	8	-3	5
18800bn1	75200be1	42300bc1	4700k1

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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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