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	6050r	Isogeny class
Conductor	6050	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	94531250 = 2 · 58 · 112	Discriminant
Eigenvalues	2+ -2 5-  1 11-  4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-13951,633048]	[a1,a2,a3,a4,a6]
Generators	[68:-33:1]	Generators of the group modulo torsion
j	6352571665/2	j-invariant
L	2.1712083270042	L(r)(E,1)/r!
Ω	1.5296748395954	Real period
R	1.4193920634653	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	48400dc2 54450gu2 6050bd2 6050bm2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050r2

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	-	1	-	4	6	-2	-3	-6	-7	-4	-9	4	9	0	6	10	-10	0	-11	-8	-12	15	17

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Quadratic twists for elliptic curve 6050r2

-4	-3	5	-11
48400dc2	54450gu2	6050bd2	6050bm2

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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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