Cremona's table of elliptic curves

142 = 2 · 71

Field	Data	Notes
Atkin-Lehner	2- 71+	Signs for the Atkin-Lehner involutions
Class	142d	Isogeny class
Conductor	142	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	568 = 23 · 71	Discriminant
Eigenvalues	2-  1  0 -1  0 -1  0 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-8,8]	[a1,a2,a3,a4,a6]
j	57066625/568	j-invariant
L	1.7333480498838	L(r)(E,1)/r!
Ω	5.2000441496513	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	1136f1 4544c1 1278e1 3550b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 142d1

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	0	-1	0	-1	0	-1	3	0	5	-4	0	-1	9	6	6	2	8	+	-1	8	12	-3	-16

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Quadratic twists for elliptic curve 142d1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-71
1136f1	4544c1	1278e1	3550b1	6958m1	17182a1	23998d1	41038m1	51262c1	75118j1	119422a1	10082j1

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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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