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	47040hd	Isogeny class
Conductor	47040	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	3415397529600000000 = 217 · 34 · 58 · 77	Discriminant
Eigenvalues	2- 3- 5- 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4782465,-4026167937]	[a1,a2,a3,a4,a6]
Generators	[-1254:825:1]	Generators of the group modulo torsion
j	784478485879202/221484375	j-invariant
L	8.5480660047128	L(r)(E,1)/r!
Ω	0.10209252738794	Real period
R	2.6165192446687	Regulator
r	1	Rank of the group of rational points
S	0.99999999999948	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	47040br6 11760f5 6720bh5	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040hd6

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	6	-4	-8	2	0	2	-10	4	0	-14	-12	-2	-4	0	-2	8	4	6	6

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Quadratic twists for elliptic curve 47040hd6

-4	8	-7
47040br6	11760f5	6720bh5

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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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