Cremona's table of elliptic curves

47600 = 2⁴ · 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	47600b	Isogeny class
Conductor	47600	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	7296	Modular degree for the optimal curve
Δ	-809200 = -1 · 24 · 52 · 7 · 172	Discriminant
Eigenvalues	2+  2 5+ 7+  5 -4 17+  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,47]	[a1,a2,a3,a4,a6]
Generators	[-22:51:8]	Generators of the group modulo torsion
j	-160000/2023	j-invariant
L	8.8165218586685	L(r)(E,1)/r!
Ω	2.3985757829208	Real period
R	1.8378660206285	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	23800d1 47600m1	Quadratic twists by: -4 5

Hecke Eigenvalues for elliptic curve 47600b1

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	+	+	5	-4	+	8	-3	-5	-4	-3	0	1	6	6	-8	4	11	1	-10	11	4	-14	-16

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Quadratic twists for elliptic curve 47600b1

-4	5
23800d1	47600m1

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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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