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	550i	Isogeny class
Conductor	550	Conductor
∏ cp	84	Product of Tamagawa factors cp
Δ	-45056000000000 = -1 · 221 · 59 · 11	Discriminant
Eigenvalues	2- -1 5+ -5 11- -2 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,7412,212781]	[a1,a2,a3,a4,a6]
Generators	[5:497:1]	Generators of the group modulo torsion
j	2882081488391/2883584000	j-invariant
L	2.2720084494269	L(r)(E,1)/r!
Ω	0.42130113036918	Real period
R	0.064200444020486	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	4400l2 17600d2 4950m2 110c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550i2

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
-	-1	+	-5	-	-2	-3	-7	6	-3	-7	7	6	-8	-6	3	-6	-1	-8	3	-2	-10	6	9	4

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Quadratic twists for elliptic curve 550i2

-4	8	-3	5	-7	-11	13
4400l2	17600d2	4950m2	110c2	26950cr2	6050h2	92950c2

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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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