Cremona's table of elliptic curves

4900 = 2² · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	4900k	Isogeny class
Conductor	4900	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	3676531250000 = 24 · 59 · 76	Discriminant
Eigenvalues	2- -2 5+ 7-  0  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-50633,4367488]	[a1,a2,a3,a4,a6]
Generators	[123:125:1]	Generators of the group modulo torsion
j	488095744/125	j-invariant
L	2.6052989223285	L(r)(E,1)/r!
Ω	0.76880815757004	Real period
R	0.56479172701181	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19600co3 78400cb3 44100bg3 980g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4900k3

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

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Quadratic twists for elliptic curve 4900k3

-4	8	-3	5	-7
19600co3	78400cb3	44100bg3	980g3	100a3

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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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