Cremona's table of elliptic curves

5550 = 2 · 3 · 5² · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 37+	Signs for the Atkin-Lehner involutions
Class	5550s	Isogeny class
Conductor	5550	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	64800	Modular degree for the optimal curve
Δ	-223724851200000000 = -1 · 218 · 310 · 58 · 37	Discriminant
Eigenvalues	2+ 3- 5-  4 -2 -4 -2 -3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,78674,-21105952]	[a1,a2,a3,a4,a6]
Generators	[1477:56861:1]	Generators of the group modulo torsion
j	137868581419655/572735619072	j-invariant
L	3.7395080163515	L(r)(E,1)/r!
Ω	0.15925943563847	Real period
R	0.39134342876449	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	44400bx1 16650ck1 5550bb1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5550s1

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
+	-	-	4	-2	-4	-2	-3	-3	0	0	+	-3	1	-6	3	-7	-8	4	-12	-9	3	8	-8	2

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Quadratic twists for elliptic curve 5550s1

-4	-3	5
44400bx1	16650ck1	5550bb1

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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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