Cremona's table of elliptic curves

2142 = 2 · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	2142d	Isogeny class
Conductor	2142	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4553386488 = 23 · 314 · 7 · 17	Discriminant
Eigenvalues	2+ 3-  2 7+  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-45711,-3750251]	[a1,a2,a3,a4,a6]
j	14489843500598257/6246072	j-invariant
L	1.3060323407156	L(r)(E,1)/r!
Ω	0.3265080851789	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17136bl4 68544bf4 714f4 53550dx4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142d3

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

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Quadratic twists for elliptic curve 2142d3

-4	8	-3	5	-7	17
17136bl4	68544bf4	714f4	53550dx4	14994bg4	36414bh4

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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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