Cremona's table of elliptic curves

4059 = 3² · 11 · 41

Field	Data	Notes
Atkin-Lehner	3- 11- 41+	Signs for the Atkin-Lehner involutions
Class	4059d	Isogeny class
Conductor	4059	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-358040331 = -1 · 38 · 113 · 41	Discriminant
Eigenvalues	-1 3-  1  1 11- -6  3  3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-302,2288]	[a1,a2,a3,a4,a6]
Generators	[18:40:1]	Generators of the group modulo torsion
j	-4165509529/491139	j-invariant
L	2.5143612622414	L(r)(E,1)/r!
Ω	1.6531501690212	Real period
R	0.25349191998793	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	64944z1 1353c1 101475bm1 44649n1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4059d1

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	-	1	1	-	-6	3	3	-3	7	-5	-7	+	2	6	0	-9	-6	-2	-6	10	4	-8	10	-12

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Quadratic twists for elliptic curve 4059d1

-4	-3	5	-11
64944z1	1353c1	101475bm1	44649n1

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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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