Cremona's table of elliptic curves

142 = 2 · 71

Field	Data	Notes
Atkin-Lehner	2+ 71+	Signs for the Atkin-Lehner involutions
Class	142b	Isogeny class
Conductor	142	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	4	Modular degree for the optimal curve
Δ	142 = 2 · 71	Discriminant
Eigenvalues	2+ -1 -2 -1 -2 -3 -6  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1,-1]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	389017/142	j-invariant
L	0.80153345214125	L(r)(E,1)/r!
Ω	4.4304737754812	Real period
R	0.18091371098437	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1136e1 4544b1 1278j1 3550j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 142b1

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	-2	-1	-2	-3	-6	5	-1	6	1	6	-6	5	-3	-6	2	-6	-14	+	-17	10	4	9	-6

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Quadratic twists for elliptic curve 142b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-71
1136e1	4544b1	1278j1	3550j1	6958b1	17182f1	23998l1	41038c1	51262i1	75118e1	119422f1	10082d1

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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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