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	550h	Isogeny class
Conductor	550	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-266200 = -1 · 23 · 52 · 113	Discriminant
Eigenvalues	2-  2 5+  4 11+ -5  0 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-23,-59]	[a1,a2,a3,a4,a6]
j	-53969305/10648	j-invariant
L	3.2349129200895	L(r)(E,1)/r!
Ω	1.0783043066965	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4400u2 17600s2 4950p2 550d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550h2

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	+	4	+	-5	0	-7	-3	3	5	4	12	-5	0	-6	12	-10	-14	3	-8	-4	15	3	13

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Quadratic twists for elliptic curve 550h2

-4	8	-3	5	-7	-11	13
4400u2	17600s2	4950p2	550d2	26950ck2	6050k2	92950p2

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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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