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	47040hc	Isogeny class
Conductor	47040	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	306019618652160000 = 220 · 34 · 54 · 78	Discriminant
Eigenvalues	2- 3- 5- 7-  4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3292865,-2300844225]	[a1,a2,a3,a4,a6]
Generators	[9775:948480:1]	Generators of the group modulo torsion
j	128031684631201/9922500	j-invariant
L	8.6654025178516	L(r)(E,1)/r!
Ω	0.11207482819008	Real period
R	4.8323755308126	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47040bq4 11760br3 6720bg4	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 47040hc4

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

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Quadratic twists for elliptic curve 47040hc4

-4	8	-7
47040bq4	11760br3	6720bg4

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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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