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	2142a	Isogeny class
Conductor	2142	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1056	Modular degree for the optimal curve
Δ	-4796983296 = -1 · 211 · 39 · 7 · 17	Discriminant
Eigenvalues	2+ 3+  1 7+  1 -3 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-474,-5068]	[a1,a2,a3,a4,a6]
Generators	[43:208:1]	Generators of the group modulo torsion
j	-599077107/243712	j-invariant
L	2.3858703787826	L(r)(E,1)/r!
Ω	0.50150981947252	Real period
R	2.3786876010643	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	17136s1 68544c1 2142l1 53550cu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142a1

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	+	1	-3	+	-2	4	0	2	-7	0	-11	-10	9	4	4	-13	-8	-1	-1	9	3	7

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Quadratic twists for elliptic curve 2142a1

-4	8	-3	5	-7	17
17136s1	68544c1	2142l1	53550cu1	14994g1	36414j1

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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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