Cremona's table of elliptic curves

6050 = 2 · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11+	Signs for the Atkin-Lehner involutions
Class	6050w	Isogeny class
Conductor	6050	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	114048	Modular degree for the optimal curve
Δ	-2357947691000000000 = -1 · 29 · 59 · 119	Discriminant
Eigenvalues	2-  1 5+ -3 11+  0 -3  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-589938,-189456508]	[a1,a2,a3,a4,a6]
j	-616295051/64000	j-invariant
L	3.0826668822836	L(r)(E,1)/r!
Ω	0.085629635618988	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48400bl1 54450bk1 1210d1 6050b1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050w1

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	+	-3	+	0	-3	3	0	9	-5	11	6	12	-6	3	12	15	-4	-3	6	12	-12	9	10

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Quadratic twists for elliptic curve 6050w1

-4	-3	5	-11
48400bl1	54450bk1	1210d1	6050b1

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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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