Cremona's table of elliptic curves

550 = 2 · 5² · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 11-	Signs for the Atkin-Lehner involutions
Class	550g	Isogeny class
Conductor	550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	60500 = 22 · 53 · 112	Discriminant
Eigenvalues	2+ -2 5-  0 11-  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-106,408]	[a1,a2,a3,a4,a6]
Generators	[3:9:1]	Generators of the group modulo torsion
j	1039509197/484	j-invariant
L	1.2030087825609	L(r)(E,1)/r!
Ω	3.4565462699076	Real period
R	0.17401890335365	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	4400x2 17600x2 4950bn2 550l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550g2

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 550g2

-4	8	-3	5	-7	-11	13
4400x2	17600x2	4950bn2	550l2	26950bo2	6050bl2	92950cs2

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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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