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	6050o	Isogeny class
Conductor	6050	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1674678757812500 = 22 · 59 · 118	Discriminant
Eigenvalues	2+  2 5-  0 11-  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-319200,-69518500]	[a1,a2,a3,a4,a6]
Generators	[2210:99020:1]	Generators of the group modulo torsion
j	1039509197/484	j-invariant
L	4.0797636875006	L(r)(E,1)/r!
Ω	0.20086107976546	Real period
R	5.07784247235	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48400de2 54450gp2 6050bl2 550l2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050o2

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	-	0	-	2	-6	-4	-2	10	-8	8	2	0	2	0	-12	10	-6	0	-6	-12	-16	18	-12

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Quadratic twists for elliptic curve 6050o2

-4	-3	5	-11
48400de2	54450gp2	6050bl2	550l2

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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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