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	2142c	Isogeny class
Conductor	2142	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	800	Modular degree for the optimal curve
Δ	-246861216 = -1 · 25 · 33 · 75 · 17	Discriminant
Eigenvalues	2+ 3+  1 7-  3 -5 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,156,-144]	[a1,a2,a3,a4,a6]
Generators	[15:66:1]	Generators of the group modulo torsion
j	15494117157/9143008	j-invariant
L	2.5079993019795	L(r)(E,1)/r!
Ω	1.0288482543665	Real period
R	0.24376765877139	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	17136p1 68544t1 2142m1 53550cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142c1

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 2142c1

-4	8	-3	5	-7	17
17136p1	68544t1	2142m1	53550cn1	14994e1	36414c1

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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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