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	256	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	-990247845888 = -1 · 216 · 38 · 72 · 47	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6864,223488]	[a1,a2,a3,a4,a6]
Generators	[-72:624:1]	Generators of the group modulo torsion
j	-35765103905346817/990247845888	j-invariant
L	4.3300175083895	L(r)(E,1)/r!
Ω	0.87632624137395	Real period
R	1.2352755469244	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	15792x1 63168b1 5922g1 49350j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974i1

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 1974i1

-4	8	-3	5	-7	-47
15792x1	63168b1	5922g1	49350j1	13818u1	92778v1

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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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