Cremona's table of elliptic curves

47775 = 3 · 5² · 7² · 13

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	47775cw	Isogeny class
Conductor	47775	Conductor
∏ cp	78	Product of Tamagawa factors cp
deg	1572480	Modular degree for the optimal curve
Δ	-6.0674662710085E+20	Discriminant
Eigenvalues	0 3- 5- 7+  2 13+  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,1429167,-985448131]	[a1,a2,a3,a4,a6]
Generators	[633:13162:1]	Generators of the group modulo torsion
j	143360000000/269440587	j-invariant
L	6.0144555943278	L(r)(E,1)/r!
Ω	0.085149255117254	Real period
R	0.9055675818805	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47775e1 47775bm1	Quadratic twists by: 5 -7

Hecke Eigenvalues for elliptic curve 47775cw1

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	+	4	-4	-4	-2	7	-7	-6	1	8	0	6	15	4	-16	-9	-11	-12	4	-5

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Quadratic twists for elliptic curve 47775cw1

5	-7
47775e1	47775bm1

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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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