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	6050bn	Isogeny class
Conductor	6050	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	21600	Modular degree for the optimal curve
Δ	-15224352343750 = -1 · 2 · 58 · 117	Discriminant
Eigenvalues	2- -2 5-  4 11- -5  0  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,5987,-58233]	[a1,a2,a3,a4,a6]
j	34295/22	j-invariant
L	2.4053561639712	L(r)(E,1)/r!
Ω	0.4008926939952	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	48400dd1 54450ds1 6050k1 550d1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050bn1

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	-	4	-	-5	0	7	3	-3	5	-4	-12	-5	0	6	12	10	14	3	-8	4	15	3	-13

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Quadratic twists for elliptic curve 6050bn1

-4	-3	5	-11
48400dd1	54450ds1	6050k1	550d1

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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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