Cremona's table of elliptic curves

53550 = 2 · 3² · 5² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	53550eb	Isogeny class
Conductor	53550	Conductor
∏ cp	1536	Product of Tamagawa factors cp
deg	1769472	Modular degree for the optimal curve
Δ	-4.059313864704E+19	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -6 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,688495,-213749503]	[a1,a2,a3,a4,a6]
Generators	[339:7480:1]	Generators of the group modulo torsion
j	3168685387909439/3563732336640	j-invariant
L	8.8515259010929	L(r)(E,1)/r!
Ω	0.10996937975912	Real period
R	0.83844607475963	Regulator
r	1	Rank of the group of rational points
S	1.0000000000029	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	17850u1 10710f1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 53550eb1

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	-6	-	4	0	2	-8	10	-2	-4	0	6	12	-2	-12	8	-2	8	4	-10	-10

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Quadratic twists for elliptic curve 53550eb1

-3	5
17850u1	10710f1

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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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