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	6050bd	Isogeny class
Conductor	6050	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	24200 = 23 · 52 · 112	Discriminant
Eigenvalues	2-  2 5+ -1 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8,1]	[a1,a2,a3,a4,a6]
Generators	[-1:3:1]	Generators of the group modulo torsion
j	18865/8	j-invariant
L	7.5099173863795	L(r)(E,1)/r!
Ω	3.4204569248063	Real period
R	0.73186297927186	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	48400ck1 54450bw1 6050r1 6050i1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050bd1

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 6050bd1

-4	-3	5	-11
48400ck1	54450bw1	6050r1	6050i1

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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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