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
deg	672	Modular degree for the optimal curve
Δ	-13310000000 = -1 · 27 · 57 · 113	Discriminant
Eigenvalues	2- -1 5+ -5 11- -2 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2213,39531]	[a1,a2,a3,a4,a6]
Generators	[-35:292:1]	Generators of the group modulo torsion
j	-76711450249/851840	j-invariant
L	2.2720084494269	L(r)(E,1)/r!
Ω	1.2639033911076	Real period
R	0.021400148006829	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	4400l1 17600d1 4950m1 110c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550i1

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 550i1

-4	8	-3	5	-7	-11	13
4400l1	17600d1	4950m1	110c1	26950cr1	6050h1	92950c1

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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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