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	2142h	Isogeny class
Conductor	2142	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	9716112 = 24 · 36 · 72 · 17	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-168,-784]	[a1,a2,a3,a4,a6]
Generators	[-7:7:1]	Generators of the group modulo torsion
j	721734273/13328	j-invariant
L	2.1147773480431	L(r)(E,1)/r!
Ω	1.3272051220572	Real period
R	0.79670328003448	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	17136z1 68544bx1 238c1 53550dp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2142h1

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	-	0	-2	+	4	0	6	0	-6	6	-12	-8	2	-4	2	12	0	2	-8	-12	-10	-14

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Quadratic twists for elliptic curve 2142h1

-4	8	-3	5	-7	17
17136z1	68544bx1	238c1	53550dp1	14994bf1	36414s1

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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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