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	47040cg	Isogeny class
Conductor	47040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	277568815104000000 = 224 · 32 · 56 · 76	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1045921,410585279]	[a1,a2,a3,a4,a6]
Generators	[-614:28665:1]	Generators of the group modulo torsion
j	4102915888729/9000000	j-invariant
L	6.5307787744649	L(r)(E,1)/r!
Ω	0.30959331429136	Real period
R	5.2736755551486	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47040ee6 1470d6 960e6	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040cg6

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	2	-6	-4	0	6	-8	-2	6	4	0	6	0	-10	4	0	-2	8	12	-18	-2

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Quadratic twists for elliptic curve 47040cg6

-4	8	-7
47040ee6	1470d6	960e6

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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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