A059765 Possible sizes of the torsion group of an elliptic curve over the rationals Q. This is a finite sequence.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16

Offset: 1

Author

Noam Katz (noamkj(AT)hotmail.com), Feb 21 2001

Keywords

• nonn
• fini
• full

Examples

			a(1) corresponds to the trivial group.
a(2) corresponds to the cyclic group C_2.
a(3) corresponds to the cyclic group C_3.
a(4) corresponds to the cyclic group C_4 and the product C_2 x C_2.
a(5) corresponds to the cyclic group C_5.
a(6) corresponds to the cyclic group C_6.
a(7) corresponds to the cyclic group C_7.
a(8) corresponds to the cyclic group C_8 and the product C_2 x C_4.
a(9) corresponds to the cyclic group C_9.
a(10) corresponds to the cyclic group C_10.
a(12) corresponds to the cyclic group C_12 and the product C_2 x C_6.
a(16) corresponds to the product C_2 x C_8.
		

References

• Joseph H. Silverman, The Arithmetic of Elliptic Curves, Graduates texts in mathematics 106 Springer-Verlag.

Links

• Index entries for sequences related to groups

Crossrefs

Cf. A221362.

Formula

Numbers n such that A221362(n) > 0. - Jonathan Sondow, May 10 2014