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	2142f	Isogeny class
Conductor	2142	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	-25040552616576 = -1 · 27 · 39 · 7 · 175	Discriminant
Eigenvalues	2+ 3- -3 7+ -1  1 17-  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-19836,1106896]	[a1,a2,a3,a4,a6]
Generators	[71:194:1]	Generators of the group modulo torsion
j	-1184052061112257/34349180544	j-invariant
L	1.8905779220521	L(r)(E,1)/r!
Ω	0.66914591702737	Real period
R	0.14126798609568	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	17136bs1 68544br1 714e1 53550du1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142f1

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	+	-1	1	-	6	2	2	0	5	-4	-9	0	-11	-4	6	-11	12	-5	-15	-1	-9	-9

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Quadratic twists for elliptic curve 2142f1

-4	8	-3	5	-7	17
17136bs1	68544br1	714e1	53550du1	14994x1	36414bj1

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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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