Cremona's table of elliptic curves

42834 = 2 · 3 · 11² · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 59+	Signs for the Atkin-Lehner involutions
Class	42834n	Isogeny class
Conductor	42834	Conductor
∏ cp	34	Product of Tamagawa factors cp
deg	2937600	Modular degree for the optimal curve
Δ	-4.8653274291104E+21	Discriminant
Eigenvalues	2+ 3-  1  2 11-  4  5  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,4027482,1258935544]	[a1,a2,a3,a4,a6]
Generators	[6698:570009:1]	Generators of the group modulo torsion
j	4078200565293477839/2746350494908416	j-invariant
L	6.7415274394174	L(r)(E,1)/r!
Ω	0.086087710508204	Real period
R	2.3032348942252	Regulator
r	1	Rank of the group of rational points
S	0.99999999999969	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	128502bx1 3894m1	Quadratic twists by: -3 -11

Hecke Eigenvalues for elliptic curve 42834n1

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
+	-	1	2	-	4	5	3	-8	-6	-8	-1	2	4	3	9	+	-10	-4	-12	-9	-16	-3	-1	14

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Quadratic twists for elliptic curve 42834n1

-3	-11
128502bx1	3894m1

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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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