Cremona's table of elliptic curves

47200 = 2⁵ · 5² · 59

Field	Data	Notes
Atkin-Lehner	2+ 5- 59-	Signs for the Atkin-Lehner involutions
Class	47200q	Isogeny class
Conductor	47200	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	27360	Modular degree for the optimal curve
Δ	-11800000000 = -1 · 29 · 58 · 59	Discriminant
Eigenvalues	2+  2 5-  1  4 -2  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1208,-16588]	[a1,a2,a3,a4,a6]
Generators	[5389356:129660362:9261]	Generators of the group modulo torsion
j	-975560/59	j-invariant
L	9.5184323620095	L(r)(E,1)/r!
Ω	0.40346329506038	Real period
R	11.795908671908	Regulator
r	1	Rank of the group of rational points
S	1.0000000000011	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	47200p1 94400dh1 47200w1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 47200q1

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	-	1	4	-2	3	0	-4	0	-10	1	9	-1	-8	0	-	-3	-15	-3	10	-11	3	12	6

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Quadratic twists for elliptic curve 47200q1

-4	8	5
47200p1	94400dh1	47200w1

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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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