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	2	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-17187500000 = -1 · 25 · 511 · 11	Discriminant
Eigenvalues	2+  1 5+ -3 11-  6  7  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,249,-6102]	[a1,a2,a3,a4,a6]
j	109902239/1100000	j-invariant
L	1.2160111663786	L(r)(E,1)/r!
Ω	0.60800558318932	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	4400n1 17600f1 4950bh1 110a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 550b1

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 550b1

-4	8	-3	5	-7	-11	13
4400n1	17600f1	4950bh1	110a1	26950w1	6050z1	92950bn1

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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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