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	4730c	Isogeny class
Conductor	4730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6768	Modular degree for the optimal curve
Δ	-26658734080 = -1 · 218 · 5 · 11 · 432	Discriminant
Eigenvalues	2+ -2 5-  0 11-  2  6  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-7338,241436]	[a1,a2,a3,a4,a6]
j	-43688964783576601/26658734080	j-invariant
L	1.1747740963659	L(r)(E,1)/r!
Ω	1.1747740963659	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	37840u1 42570t1 23650o1 52030z1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4730c1

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	-	2	6	6	6	2	0	-2	-6	-	2	12	-12	6	-4	16	2	6	-4	-2	-2

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Quadratic twists for elliptic curve 4730c1

-4	-3	5	-11
37840u1	42570t1	23650o1	52030z1

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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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