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	550j	Isogeny class
Conductor	550	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	176	Modular degree for the optimal curve
Δ	-2816000 = -1 · 211 · 53 · 11	Discriminant
Eigenvalues	2- -3 5- -1 11+  0 -5 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-15,87]	[a1,a2,a3,a4,a6]
Generators	[-1:10:1]	Generators of the group modulo torsion
j	-2803221/22528	j-invariant
L	1.9169774850456	L(r)(E,1)/r!
Ω	2.1835005397946	Real period
R	0.03990625999	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	4400bd1 17600bj1 4950u1 550e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550j1

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
-	-3	-	-1	+	0	-5	-7	-8	3	-5	-1	-8	10	0	-1	12	5	-4	-7	2	-4	0	-7	8

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Quadratic twists for elliptic curve 550j1

-4	8	-3	5	-7	-11	13
4400bd1	17600bj1	4950u1	550e1	26950df1	6050t1	92950bk1

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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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