Cremona's table of elliptic curves

4760 = 2³ · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	4760b	Isogeny class
Conductor	4760	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	7392	Modular degree for the optimal curve
Δ	-687820000000 = -1 · 28 · 57 · 7 · 173	Discriminant
Eigenvalues	2+  2 5+ 7+ -2  1 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4681,-128019]	[a1,a2,a3,a4,a6]
Generators	[105:726:1]	Generators of the group modulo torsion
j	-44319254354944/2686796875	j-invariant
L	4.7248921761911	L(r)(E,1)/r!
Ω	0.28757743261739	Real period
R	4.1074956170825	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	9520b1 38080o1 42840ca1 23800j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4760b1

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	+	+	-2	1	+	6	-3	-6	3	-9	11	-12	-3	-6	2	-7	-10	8	4	-12	9	2	-8

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Quadratic twists for elliptic curve 4760b1

-4	8	-3	5	-7	17
9520b1	38080o1	42840ca1	23800j1	33320g1	80920i1

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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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