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	4760a	Isogeny class
Conductor	4760	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	10304	Modular degree for the optimal curve
Δ	-205891532564480 = -1 · 211 · 5 · 72 · 177	Discriminant
Eigenvalues	2+ -1 5+ 7+  2  1 17+  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6536,-717524]	[a1,a2,a3,a4,a6]
Generators	[1434:15673:8]	Generators of the group modulo torsion
j	-15079826167058/100532974885	j-invariant
L	2.7908539827184	L(r)(E,1)/r!
Ω	0.23619266044541	Real period
R	5.9080031899709	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	9520a1 38080n1 42840cc1 23800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4760a1

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	1	+	1	-6	5	7	6	-6	-8	3	9	1	-11	-4	1	-11	4	2	5	7

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Quadratic twists for elliptic curve 4760a1

-4	8	-3	5	-7	17
9520a1	38080n1	42840cc1	23800h1	33320f1	80920g1

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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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