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

Author

Arkadiusz Wesolowski, Aug 24 2013

Keywords

• easy
• sign

References

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

Links

• 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

Crossrefs

Cf. A000290, A062838, A179126.

Formula

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

a(A179126(n)) = 3.