Cremona's table of elliptic curves

47040 = 2⁶ · 3 · 5 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7-	Signs for the Atkin-Lehner involutions
Class	47040bl	Isogeny class
Conductor	47040	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	1561324584960000 = 218 · 34 · 54 · 76	Discriminant
Eigenvalues	2+ 3+ 5- 7-  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31425,1002177]	[a1,a2,a3,a4,a6]
Generators	[-93:1764:1]	Generators of the group modulo torsion
j	111284641/50625	j-invariant
L	5.8660863299671	L(r)(E,1)/r!
Ω	0.42661367867999	Real period
R	1.7187934374663	Regulator
r	1	Rank of the group of rational points
S	0.99999999999641	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47040hg3 735e4 960g3	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040bl3

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
+	+	-	-	4	-2	-2	4	0	2	0	10	-10	-4	-8	10	-4	-2	-12	-8	-10	0	12	6	-2

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Quadratic twists for elliptic curve 47040bl3

-4	8	-7
47040hg3	735e4	960g3

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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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