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	550l	Isogeny class
Conductor	550	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	945312500 = 22 · 59 · 112	Discriminant
Eigenvalues	2-  2 5-  0 11- -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2638,51031]	[a1,a2,a3,a4,a6]
j	1039509197/484	j-invariant
L	3.0916289707547	L(r)(E,1)/r!
Ω	1.5458144853773	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4400y2 17600z2 4950q2 550g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550l2

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 550l2

-4	8	-3	5	-7	-11	13
4400y2	17600z2	4950q2	550g2	26950dj2	6050o2	92950bb2

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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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