This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A221362 #26 Feb 24 2023 11:25:15 %S A221362 1,1,1,2,1,1,1,2,1,1,0,2,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A221362 0,0,0 %N A221362 Number of distinct groups of order n that are the torsion subgroup of an elliptic curve over the rationals Q. %C A221362 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. %D A221362 J. H. Silverman, The Arithmetic of Elliptic Curves, Graduates Texts in Mathematics 106, Springer-Verlag, 1986 (see Theorem 7.5). %H A221362 B. Mazur, <a href="http://dx.doi.org/10.1007/BF01390348">Rational isogenies of prime degree</a>, Inventiones Math. 44, 2 (June 1978), 129-162. %H A221362 Wikipedia, <a href="http://en.wikipedia.org/wiki/Elliptic_curve">Elliptic curve</a> %H A221362 Wikipedia, <a href="http://en.wikipedia.org/wiki/Mazur%27s_torsion_theorem">Mazur's torsion theorem</a> %F A221362 a(n) = 0 for n > 16. %F A221362 a(A059765(n)) > 0. - _Jonathan Sondow_, May 10 2014 %e A221362 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. %Y A221362 Cf. A059765 (possible sizes of the torsion subgroup of an elliptic curve over Q), A146879. %K A221362 nonn,fini,full,easy %O A221362 1,4 %A A221362 _Jonathan Sondow_, Jan 12 2013