Cremona's table of elliptic curves

1974 = 2 · 3 · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 47+	Signs for the Atkin-Lehner involutions
Class	1974i	Isogeny class
Conductor	1974	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	4050776146821264 = 24 · 32 · 78 · 474	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-111264,13943664]	[a1,a2,a3,a4,a6]
Generators	[266:1652:1]	Generators of the group modulo torsion
j	152330884252627401217/4050776146821264	j-invariant
L	4.3300175083895	L(r)(E,1)/r!
Ω	0.43816312068697	Real period
R	4.9411021876975	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15792x4 63168b3 5922g4 49350j3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974i3

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

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Quadratic twists for elliptic curve 1974i3

-4	8	-3	5	-7	-47
15792x4	63168b3	5922g4	49350j3	13818u4	92778v3

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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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