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	1974f	Isogeny class
Conductor	1974	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	-191020032 = -1 · 210 · 34 · 72 · 47	Discriminant
Eigenvalues	2- 3+  0 7- -6  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-48,657]	[a1,a2,a3,a4,a6]
Generators	[-3:29:1]	Generators of the group modulo torsion
j	-12246522625/191020032	j-invariant
L	3.7028107777073	L(r)(E,1)/r!
Ω	1.5148479844634	Real period
R	0.24443447894998	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	15792bc1 63168bk1 5922j1 49350ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1974f1

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
-	+	0	-	-6	0	-2	-2	-4	0	0	2	-6	2	+	-6	0	14	-2	-8	-6	-16	-12	6	10

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Quadratic twists for elliptic curve 1974f1

-4	8	-3	5	-7	-47
15792bc1	63168bk1	5922j1	49350ba1	13818bh1	92778o1

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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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