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	6050a	Isogeny class
Conductor	6050	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-1064800 = -1 · 25 · 52 · 113	Discriminant
Eigenvalues	2+  0 5+ -2 11+  1  2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-17,61]	[a1,a2,a3,a4,a6]
Generators	[3:4:1]	Generators of the group modulo torsion
j	-16875/32	j-invariant
L	2.5839741930104	L(r)(E,1)/r!
Ω	2.4639496648627	Real period
R	0.52435612420564	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	48400bg1 54450fc1 6050bh1 6050v1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050a1

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	+	-2	+	1	2	-5	5	5	5	0	-10	1	0	10	-6	10	10	3	6	-10	-11	-5	5

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Quadratic twists for elliptic curve 6050a1

-4	-3	5	-11
48400bg1	54450fc1	6050bh1	6050v1

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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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