Cremona's table of elliptic curves

42042 = 2 · 3 · 7² · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	42042df	Isogeny class
Conductor	42042	Conductor
∏ cp	960	Product of Tamagawa factors cp
deg	2211840	Modular degree for the optimal curve
Δ	-1.4646816608415E+21	Discriminant
Eigenvalues	2- 3-  0 7- 11+ 13- -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5789498,5668663524]	[a1,a2,a3,a4,a6]
Generators	[2836:-111242:1]	Generators of the group modulo torsion
j	-182414014585448388625/12449588698939392	j-invariant
L	11.004528776892	L(r)(E,1)/r!
Ω	0.1487570734036	Real period
R	0.30823544849282	Regulator
r	1	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	126126cx1 6006u1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 42042df1

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

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Quadratic twists for elliptic curve 42042df1

-3	-7
126126cx1	6006u1

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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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