A228532 a(n) = order of the torsion subgroup of the elliptic curve y^2 = x^3 + n if n is a sixth-power-free integer, otherwise -1.

6, 0, 0, 3, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0

Offset

1,1

References

Dale Husemoller, Elliptic Curves, Graduate Texts in Mathematics 111, Springer-Verlag, 2004, pp. 35-37.

Links

Table of n, a(n) for n=1..87.

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Wikipedia, Torsion subgroup

Formula

a(A062838(n)) = 2 for n > 1.

a(A179126(n)) = 3.

Crossrefs

Cf. A000290, A062838, A179126.

Sequence in context: A337885 A333204 A186978 * A019956 A212720 A114760

Adjacent sequences: A228529 A228530 A228531 * A228533 A228534 A228535

Keyword

easy,sign

Author

Arkadiusz Wesolowski, Aug 24 2013

Status

approved