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	550b	Isogeny class
Conductor	550	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	-25164218750 = -1 · 2 · 57 · 115	Discriminant
Eigenvalues	2+  1 5+ -3 11-  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-148501,-22038602]	[a1,a2,a3,a4,a6]
j	-23178622194826561/1610510	j-invariant
L	1.2160111663786	L(r)(E,1)/r!
Ω	0.12160111663786	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	4400n2 17600f2 4950bh2 110a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550b2

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	+	-3	-	6	7	5	6	5	-3	-3	2	-4	2	1	-10	7	-8	7	-14	10	6	-15	12

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Quadratic twists for elliptic curve 550b2

-4	8	-3	5	-7	-11	13
4400n2	17600f2	4950bh2	110a2	26950w2	6050z2	92950bn2

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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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