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	2142m	Isogeny class
Conductor	2142	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	-179961826464 = -1 · 25 · 39 · 75 · 17	Discriminant
Eigenvalues	2- 3+ -1 7- -3 -5 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,1402,2485]	[a1,a2,a3,a4,a6]
Generators	[19:179:1]	Generators of the group modulo torsion
j	15494117157/9143008	j-invariant
L	4.155301638611	L(r)(E,1)/r!
Ω	0.61627968409256	Real period
R	0.13485116403697	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	17136m1 68544n1 2142c1 53550c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142m1

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	-	-3	-5	+	-6	8	-4	-6	-5	4	1	-2	3	-4	-8	-1	-8	-5	9	9	7	3

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Quadratic twists for elliptic curve 2142m1

-4	8	-3	5	-7	17
17136m1	68544n1	2142c1	53550c1	14994bu1	36414bq1

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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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