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

1,2

References

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

Links

Table of n, a(n) for n=1..12.

Index entries for sequences related to groups

Formula

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

Example

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.

Crossrefs

Cf. A221362.

Sequence in context: A005711 A322856 A280863 * A180479 A193456 A143289

Adjacent sequences: A059762 A059763 A059764 * A059766 A059767 A059768

Keyword

nonn,fini,full

Author

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

Status

approved