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	47040ha	Isogeny class
Conductor	47040	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	1423082304000000 = 212 · 33 · 56 · 77	Discriminant
Eigenvalues	2- 3- 5- 7- -2 -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-41225,-2675625]	[a1,a2,a3,a4,a6]
Generators	[-110:735:1]	Generators of the group modulo torsion
j	16079333824/2953125	j-invariant
L	7.3381511786706	L(r)(E,1)/r!
Ω	0.3392923743752	Real period
R	0.6007725140197	Regulator
r	1	Rank of the group of rational points
S	0.99999999999877	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	47040fe2 23520b1 6720be2	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040ha2

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	-4	2	-6	-4	10	-2	2	10	-4	8	-4	4	-2	-4	6	0	-4	-4	6	-4

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Quadratic twists for elliptic curve 47040ha2

-4	8	-7
47040fe2	23520b1	6720be2

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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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