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	2142b	Isogeny class
Conductor	2142	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-314874 = -1 · 2 · 33 · 73 · 17	Discriminant
Eigenvalues	2+ 3+  3 7-  3  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-168,882]	[a1,a2,a3,a4,a6]
j	-19486825371/11662	j-invariant
L	2.0155387870874	L(r)(E,1)/r!
Ω	3.0233081806311	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	17136o1 68544q1 2142n2 53550cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142b1

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
+	+	3	-	3	5	+	2	0	0	2	-1	0	5	-6	-3	-12	8	11	-12	-7	-7	-3	-9	17

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Quadratic twists for elliptic curve 2142b1

-4	8	-3	5	-7	17
17136o1	68544q1	2142n2	53550cq1	14994k1	36414f1

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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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