Cremona's table of elliptic curves

4700 = 2² · 5² · 47

Field	Data	Notes
Atkin-Lehner	2- 5- 47+	Signs for the Atkin-Lehner involutions
Class	4700h	Isogeny class
Conductor	4700	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-648893750000 = -1 · 24 · 58 · 473	Discriminant
Eigenvalues	2-  1 5- -1  0  2  3  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,2042,16213]	[a1,a2,a3,a4,a6]
Generators	[4179:54431:27]	Generators of the group modulo torsion
j	150590720/103823	j-invariant
L	4.2505115747655	L(r)(E,1)/r!
Ω	0.574834893002	Real period
R	7.3943172665943	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18800bq2 75200bi2 42300be2 4700d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4700h2

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
-	1	-	-1	0	2	3	2	-6	-6	2	-10	6	-4	+	6	-9	-10	14	3	14	-16	-3	6	-10

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Quadratic twists for elliptic curve 4700h2

-4	8	-3	5
18800bq2	75200bi2	42300be2	4700d2

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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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