Cremona's table of elliptic curves

50562 = 2 · 3² · 53²

Field	Data	Notes
Atkin-Lehner	2+ 3- 53-	Signs for the Atkin-Lehner involutions
Class	50562r	Isogeny class
Conductor	50562	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-111136084992 = -1 · 210 · 36 · 533	Discriminant
Eigenvalues	2+ 3-  2  2  2 -1  3 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-21276,-1189296]	[a1,a2,a3,a4,a6]
Generators	[808808:18883356:1331]	Generators of the group modulo torsion
j	-9814089221/1024	j-invariant
L	6.0218224382175	L(r)(E,1)/r!
Ω	0.19764843873035	Real period
R	7.6168353224771	Regulator
r	1	Rank of the group of rational points
S	1.0000000000004	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5618i2 50562bj2	Quadratic twists by: -3 53

Hecke Eigenvalues for elliptic curve 50562r2

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	2	2	-1	3	-1	-9	5	0	7	0	6	12	-	0	-10	-8	5	-14	-11	9	-10	-7

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Quadratic twists for elliptic curve 50562r2

-3	53
5618i2	50562bj2

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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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