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	4730f	Isogeny class
Conductor	4730	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-189200 = -1 · 24 · 52 · 11 · 43	Discriminant
Eigenvalues	2- -1 5+ -2 11-  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-6,19]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	-24137569/189200	j-invariant
L	4.1782200904812	L(r)(E,1)/r!
Ω	2.7361071532293	Real period
R	0.19088342746144	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	37840l1 42570m1 23650g1 52030e1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4730f1

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	+	-2	-	4	0	-2	-2	3	4	-4	8	+	-2	-9	-8	-13	14	-4	-13	-13	9	-8	3

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Quadratic twists for elliptic curve 4730f1

-4	-3	5	-11
37840l1	42570m1	23650g1	52030e1

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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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