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	4730d	Isogeny class
Conductor	4730	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-10073008000 = -1 · 27 · 53 · 114 · 43	Discriminant
Eigenvalues	2-  0 5+  3 11+  1 -4 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-478,-6163]	[a1,a2,a3,a4,a6]
Generators	[65:451:1]	Generators of the group modulo torsion
j	-12054670471089/10073008000	j-invariant
L	5.3761686294696	L(r)(E,1)/r!
Ω	0.49316025251562	Real period
R	0.77867598413145	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	37840n1 42570o1 23650b1 52030b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4730d1

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	+	3	+	1	-4	-7	4	3	-9	-4	-3	-	-2	-14	12	1	-3	6	-7	-11	-16	4	-2

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Quadratic twists for elliptic curve 4730d1

-4	-3	5	-11
37840n1	42570o1	23650b1	52030b1

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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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