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	6050bg	Isogeny class
Conductor	6050	Conductor
∏ cp	13	Product of Tamagawa factors cp
deg	37440	Modular degree for the optimal curve
Δ	9680000000000 = 213 · 510 · 112	Discriminant
Eigenvalues	2- -2 5+  3 11-  0  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-135638,-19238108]	[a1,a2,a3,a4,a6]
Generators	[-212:122:1]	Generators of the group modulo torsion
j	233551483825/8192	j-invariant
L	4.5914489560712	L(r)(E,1)/r!
Ω	0.24877406787003	Real period
R	1.4197154239596	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	48400cj1 54450cb1 6050q1 6050l1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6050bg1

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	+	3	-	0	2	-2	-9	-2	-3	-12	7	-8	11	-8	-10	-10	10	-8	11	8	12	-9	-9

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Quadratic twists for elliptic curve 6050bg1

-4	-3	5	-11
48400cj1	54450cb1	6050q1	6050l1

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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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