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	2142g	Isogeny class
Conductor	2142	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1.5303528939174E+23	Discriminant
Eigenvalues	2+ 3-  2 7- -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2633436,18893883640]	[a1,a2,a3,a4,a6]
Generators	[3015:194335:1]	Generators of the group modulo torsion
j	-2770540998624539614657/209924951154647363208	j-invariant
L	2.5663010016199	L(r)(E,1)/r!
Ω	0.084663132502506	Real period
R	7.5779767584903	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17136y6 68544ca5 714g6 53550dt5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142g6

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	-	-4	-2	+	4	-8	-6	0	-2	-10	-4	0	-6	4	6	-12	8	-6	0	12	6	2

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Quadratic twists for elliptic curve 2142g6

-4	8	-3	5	-7	17
17136y6	68544ca5	714g6	53550dt5	14994bi6	36414t5

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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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