OFFSET
1,4
COMMENTS
Barry Mazur proved that the torsion subgroup of an elliptic curve over Q is one of the 15 following groups: Z/NZ for N = 1, 2, …, 10, or 12, or Z/2Z × Z/2NZ with N = 1, 2, 3, 4.
REFERENCES
J. H. Silverman, The Arithmetic of Elliptic Curves, Graduates Texts in Mathematics 106, Springer-Verlag, 1986 (see Theorem 7.5).
LINKS
B. Mazur, Rational isogenies of prime degree, Inventiones Math. 44, 2 (June 1978), 129-162.
Wikipedia, Elliptic curve
Wikipedia, Mazur's torsion theorem
FORMULA
a(n) = 0 for n > 16.
a(A059765(n)) > 0. - Jonathan Sondow, May 10 2014
EXAMPLE
a(4) = 2 because a subgroup of order 4 in an elliptic curve over Q is isomorphic to one of the 2 groups Z/4Z or Z/2Z × Z/2Z.
CROSSREFS
KEYWORD
nonn,fini,full,easy
AUTHOR
Jonathan Sondow, Jan 12 2013
STATUS
approved