Cremona's table of elliptic curves

4730 = 2 · 5 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 43-	Signs for the Atkin-Lehner involutions
Class	4730k	Isogeny class
Conductor	4730	Conductor
∏ cp	686	Product of Tamagawa factors cp
deg	219520	Modular degree for the optimal curve
Δ	-360317791790000000 = -1 · 27 · 57 · 117 · 432	Discriminant
Eigenvalues	2- -3 5-  1 11-  0 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5582262,5077966149]	[a1,a2,a3,a4,a6]
Generators	[-2493:60371:1]	Generators of the group modulo torsion
j	-19237750463016353596082481/360317791790000000	j-invariant
L	3.8241488940115	L(r)(E,1)/r!
Ω	0.27814414800152	Real period
R	0.9820573051492	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	7	Number of elements in the torsion subgroup
Twists	37840w1 42570g1 23650f1 52030m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4730k1

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
-	-3	-	1	-	0	-3	-1	-4	-5	-3	-11	0	-	6	-9	4	13	12	9	-10	-4	0	-1	0

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Quadratic twists for elliptic curve 4730k1

-4	-3	5	-11
37840w1	42570g1	23650f1	52030m1

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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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