login
A059765
Possible sizes of the torsion group of an elliptic curve over the rationals Q. This is a finite sequence.
11
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.
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
KEYWORD
nonn,fini,full
AUTHOR
Noam Katz (noamkj(AT)hotmail.com), Feb 21 2001
STATUS
approved